A kappa is at least 100 billion times longer than the estimated age of our visible universe

The Watercooler
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I thought I would share here what comes to light if we take some suttas literally.

SN 15.5:

“Suppose there was a huge stone mountain, a league long, a league wide, and a league high, with no cracks or holes, one solid mass. And as each century passed someone would stroke it once with a fine cloth from Kāsi. By this means the huge stone mountain would be worn away before the eon comes to an end.

Apparently a single stroke of a cloth on a rock could not remove more than 10 micrograms.

If we consider very conservatively that a “league” is 6 km long, and we consider the mountain to be roughly a cone, that makes its volume 1/3 × π × ( 6 × 10^3)^3 = 2.26 × 10^11 m^3

The lightest mountain rocks weigh about 2 tons per cube meter, which makes 4.5 × 10^14 kg for our mountain.

Counting 10 micrograms removed per stroke of the cloth, that makes 4.5 × 10^19 strokes of the cloth, and counting 100 years per stroke of the cloth, that makes 4.5 × 10^21 years to wear away the whole mountain (assuming it would remain otherwise unchanging of course).

The estimated age of the universe is about 14 billion years.

4.5 × 10^21 / (14 × 10^9) = 3 × 10^11

If we’re still being even more conservative, that represents at least 100 billion times the estimated age of our universe.

So when the scriptures talk of eons of expansion or contraction of the universe, it has nothing to do with the redshift and the expansion of our universe modern cosmology suggests.

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This Wikipedia article comparing the Purānic and Buddhist concept of Kalpa/kappa might be of interest to you. Ancient Indian literature is full of such big or small numbers, sometimes bizarrely specific and sometimes strangely vague.

Kalpa/Kappa

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Thank you for the reference. The numbers I have seen there vary between 16 million years and about 300 trillion years. Interestingly, all of these are dwarfed at least a billionfold by the numbers suggested in this sutta

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A kalpa is not an exact period, it is usually used with the sense of an extremely high (unspecific) number of years.

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This sort of calculation always seems to me to be overthinking the message, which I take to be: “This is a big number.”

As @srkiris says:

There are similar issues with discussions of the duration of mind moments in the commentaries.

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May I ask, is it your opinion that the image of a mountain being eroded away by a silk cloth is one that ought to be taken literally? That is, the Buddha intended that it be taken so?

But only if we insist on literalism in the matter. If instead we take the mountain and silk cloth image in some non-literal way (e.g., as a rhetorical adynaton), then the claimed compatibility of Buddhist cosmological conceptions with those of modern physics would remain at least a possibility.

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Yes this is an example of alaṅkāra (figure of speech) called atiśayokti (hyperbole) in the Indic traditions. There are about 20 other figures of speech listed in ancient works of rhetoric.

Update: There are actually more than 21, but on this topic see Alamkaras mentioned by Vamana

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edit: sorry - off topic

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Hi Silence. Hope that you are well?

I don’t get your conclusion here. I’m not the most scientific or arithmetically able person here, so please bare with me. I would really like to try and understand why you think this is so.

Let me start with trying to understand if we are on the same page.

Your suggestion is that the (Buddhist) aeon is very much bigger than the current age of the universe. Is that right? And because of that calculation you come to the conclusion above. Is that also right?

As far as I know, according to modern cosmology, 14 billion years in from the big bang, we observe that the universe is still expanding and this expansion is accelerating and (according to modern cosmology) the universe is expected to continue to expand. Is that right?

Now Buddhist theory might suggest that there would be a period of expansion followed by a period of contraction in alignment with a big-bounce model. Each period of expansion/contraction would be called a (Buddhist) aeon. Is that your understanding too?

Now if a big-bounce model is correct, then the universe still has to slow-down acceleration, slow down expansion, stop expanding and then contract. The length of time for these things to occur is unknown by modern cosmologists. Who knows, it might be in line with your calculations?

But the big-bounce isn’t the modern cosmologists favoured position. That would be the heat death of the universe. In this scenario we get some very big numbers that might be approaching (or exceeding) your calculations:

For example:

Star formation ceases
10^12–14 (1–100 trillion) years
…
Planets fall or are flung from orbits by a close encounter with another star
10^15 (1 quadrillion) years
…
Stellar remnants escape galaxies or fall into black holes
10^19 to 10^20 (10 to 100 quintillion) years
…
Possible ionization of matter
10^23 years from now
…

from Future of an expanding universe - Wikipedia

The numbers get much bigger from there on.

Given this, I don’t understand how you have drawn the conclusion that you do?

And I haven’t even got onto the quality of cloth from Kāsi yet :wink:

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I think it is important to examinate critically anything we accept as true. There are many suttas where great care is given to not making false statements, so it is surprising to see such things being said. It is my opinion that we must give thought to these inconvenient oddities rather than dismissing them without giving them much thought. Inconvenient oddities sometimes turn out to be signs of something we should pay attention to.

Here my takeaway is that suttas on this topic must be taken with a grain of salt. This is important in my view because there are people who think they should not be taken with any grain of salt.

My opinion is that if the Buddha did say “the huge stone mountain would be worn away before the eon comes to an end”, I would expect the eon not to come to an end before the huge stone mountain would be worn away. Otherwise that would be false speech.

It doesn’t seem to me that the Buddha was using hyperbole, even less hyper-hyperbole when speaking (other than perhaps as jokes, which doesn’t seem to be the case here). I would rather think he would not encourage people to speak in hyperboles that can easily be misinterpreted (which often happens in religion, it seems).

The 32 marks of a great man would imo fit the definition adynaton, and in my view they have little worth in helping us get to the end of suffering.

Hi stu, I am doing well, thank you. Hope you are too :slight_smile:

According to this sutta, yes

Yes because otherwise we have to assume that something extremely unlikely has happened (that we would happen to be in the first 1/100 billionth of a kappa).

In the short to medium term, yes. Beyond that no one really knows.

yes

Maybe but then again we would be assuming that we are the very beginning of a kappa.

Yes indeed. But it’s not like these considerations are falsifiable, so they hardly qualify as science anyway. It’s more like opinions

I don’t know what exactly it is that you don’t understand. Neither the sutta nor the OP talk about the heat death of the universe.

All I am saying is:

  1. Such suttas must be taken with a grain of salt
  2. We should not confuse the Buddhist concepts of contraction and expansion of the universe with modern science’s concepts of contraction and expansion of the visible universe.
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Is there any reason to assume from the suttas that it isn’t the case?

To note, I do share your concerns and care with literal interpretation of everything in the suttas; some are obvious metaphors (like yeshe pointed earlier, burning chaffe). But we might just be at the beginning of a kalpa.

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There’s a one in at least a hundred billion chances that it is the case, assuming the present day could in theory be anywhere in a kappa. Why conveniently in its first 1/100 000 000 000 th part?

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Eh? Isn’t it the same probability for any certain spot in the kappa? Is any spot favored over any other?? What is ‘convenient’ about it??!!

:pray:

PS: Also, here I’d like to mention Sir Roger Penrose’s Conformal Cyclic Cosmology which both predicts the heat death of the universe but is also cyclic :slight_smile: In fact, it is the heat death of the universe which allows Penrose to map the end end with a new era of cosmic expansion beginning through a conformally invariant transformation :joy:

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If we can just agree that a kalpa is a loooong time… somewhere in the suttas, The Buddha talks about previous Buddhas in previous kalpas. Humans haven’t been around for a kalpa - for previous Buddhas to have existed on this planet.

So, were the previous Buddhas on other planets, or were they in previous Big-Bang/Crunch cycles? Can any knowledge carry on from one big bang instance, to a subsequent big bang instance?

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Why so many Kappas?

It is not in intention mean spirited Hyperbole.

It is however a literary device intended to discourage people from trying to settle into a frame of mind that thinks it can grasp and contain things that are immeasurable by quality, not just number.

The Vimuttimagga says Arthats with the Divine Eye can review many incarnations. Paccecabuddhas can review thousands. And Tathagatas can review an infinite number.

The idea is to not profane sacred gualities with oordinary thinking.

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There are obviously different possibly ways of approaching the Dhamma, but personally, I don’t find it useful to think of the cosmology of the suttas as literally true and accurate in the sense of modern measurements. I recall my disillusionment with the book The Tao of Physics back in the 70s when I found out that the author was relying on a particle physics model that was rapidly falling out of fashion (as the “Standard Model” took over). I don’t base my faith in Buddha-Dhamma on finding connections with science - I don’t think that’s the point of it. Besides, science is a moving target. For example, one of the current fashions in cosmology is “dark energy”. It is quite likely that that will be superseded by another interpretation in due course, so trying to find connections between dark energy and Dhamma would also lead to disappointment.

I’m not advocating not taking the stories in the suttas seriously (apologies for the double negative). The contain valuable information. However, I’m skeptical of the usefulness of interpreting that information in terms of current scientific models.

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No apologies necessary as long as you understand that a double negative does not need to be interpreted as a positive! :joy:

In other words, we readers are not obligated to interpret your double negative as advocation for taking the suttas seriously :rofl: :pray:

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Agreed, this is what I demonstrated in the OP

It’s not so much finding connections as identifying potential contradictions. If the suttas were to tell us for example that the speed of light is infinite, we would know they’d be empirically wrong about that.

Why is that important? Well personally the only reason why I am interested in this teaching is because of its ability to and accuracy in describing the reality of our lives. The point is that it seems to be very accurate in terms of describing our psychological, subjective reality (the very thing that largely escapes modern science btw), but when it starts describing the universe it’s better to take it with a grain of salt, as you also suggest.

So it seems to me we essentially agree

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Fantastic Silence! I doing great. Just had a lovely couple of months off line and just finding my feet on the internet again.

Good that we appear to be on the same page.

I don’t think that this is unlikely. I tend to agree (to some extent) with @yeshe.tenley when they say:

If all things were equal, then we would say that being anywhere in the kappa is equally probable. But we do have some observations that might suggest that we are in an early period. First we see that the universe is expanding rather than contracting. So we might suggest that we are more likely to be in the first half of the kappa. Then we know that the expansion is accelerating, so that might suggest that we are closer to the beginning of the expansion than the end of it. Then we know that the acceleration is still increasing, so that suggests that we are even closer to the beginning.

:rofl: Well, yes, quite. But I guess that they are best guesses from Cosmologists, which might add some weight to their opinions.

No, that’s right. But the OP talks about “modern cosmology” and in modern cosmology ‘Heat Death’ is the consensus, so we have some best guess figures for the sort of lengths of time we are talking about, which we don’t have (afaik for the big-bounce models). That’s why I brought it in—just as a general understanding of the time spans involved according to (the opinions of) modern cosmologists. In general I’m more inclined to think that the consensus of ‘Heat Death’ amongst Cosmologists will turn out to be wrong.

Fair enough.

I think that it can be taken on a number of levels and one of those can indeed equate these two concepts.

I don’t think that your calculations have shown that …

To the contrary, I am now rather more inclined to agree that they just might be talking about the same concepts.

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Ockham’s razor suggests otherwise since we have a 99.999999999% chance to not be in the first 0.000000001% of an eon. But you are free to think however you see fit