Infinity Problem

I’m not sure how much detail there is in EBTs, but the traditional Buddhist presentation is that liberation is impossible while a being is in the lower realms below the human world or in the higher realms in the heavens. So, the actually number of lives when there’s a possibility of liberation is a subset that’s less than infinity, if we really want to take it to this extreme of mathematically calculating it. (Is there some mathematics for infinite subsets of infinity? I have no idea myself.) There’s also the later idea that a person can liberate themselves without encountering a Buddha by realized the truth of dependent origination in other ways (i.e., become a pratyeka-buddha), which would raise the chances a bit more.

Interestingly, in later Buddhist thought, it was asserted that it’s a certainty that each being will eventually be liberated because suffering is the primary cause for developing wisdom and seeking liberation from it. The only uncertainty is the duration of time spent in samsara.

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The amount of times a person has taken birth is infinite.

The amount of times a person has taken birth as a human is also infinite.

The amount of times a person has taken birth as a female is infinite.

Infinities can be measurably smaller than other infinities whilst remaining uncountable, see my first post. There is a difference between measuring and counting or something being immeasurable or uncountable.


It’s “without discoverable beginning” not “no beginning”. One is epistemological, the other metaphysical.


Buddha taught that there is no point where not having been delusion arose to fire up existence.

If one holds that there could be such a point then one will hold that it is possible that having become extinguished a being will become reborn.

In as far as there is delusion there is transmigation and it doesn’t stop until it is extinguished.

Having become extinguished it doesn’t arise as there is no fuel for a future.

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Was about to make a similar point! :slight_smile:
It’s not clear we are actually talking about infinities here. MN 63 also comes to mind where the Buddha refuses to state whether the statement “the cosmos is eternal” is true or not.

In response to the OP, the biological example of the evolution of life here on earth comes to mind. If one could trace the ancestors of every person on this forum :slight_smile: going back to our ape-like ancestors, through the small mammal like creatures existing at the time of the dinosaurs, going all the way back to very start of life on earth, it would number in billions of generations, gradually getting to simpler and simpler forms of life. Near the beginning we would get to a grey area between life and non-life where some very simple kinds of self-replicating chemical reactions would be starting to get going. Pretty vast (if one started merely counting these generations, an entire human life would be long over before even getting a fraction of the way there), but not infinite. Maybe today’s nematode or simple organism will eventually be a sentient being quite a large number eons down the road! :wink: :man_shrugging: Instead of these chains of rebirths being eternal, perhaps they spontaneously start with very simple life forms (in something that could barely be called life) and persist for perhaps vast periods, but maybe not forever! :man_shrugging: This is rather speculative, but just pointing out that infinity is not the only possibility here, and the Buddha refused to give definitive answers on many such metaphysical questions.


But still you can calculate the likelyhood. If you cannot see and know in which state the house is and you are at some stage of building in this life, it is very likely that the house is not finished in this life and much more likely then it would be that it is and the likelyhood is equivalent to the time it takes to build the house.

The argument is the same as saying when you throw a coin you cannot say the chance it lands on head is 50:50 because it is not random it depends on the force it was thrown with, the speed it was flipped with, the height it was thrown in the air and so on, but still you can say it is 50:50.

I am not going to repeat myself. I already explained this thing with building a house several times.

You are confusing physics and mathematics here.

Mathematics is the general case of a coinflip whereas physics is the special case or a particular coinflip.

You can’t use the general statement to explain a particular case.

In the general case a coin is imaginary and is perfectly weighted, therefore it is a fair coinflip in mathematics.

Whereas the physics of a particular coinflip aren’t random.

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I have explained why I don’t think your example with building a house is correct.
But still, thanks for your help.

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Does anyone want to try to find a solution?

Sharing my thoughts:
Maybe Infinite lifes and the possibility of enlightenment being calculated out of the infinity is impossible because Infinity is not possible to be fully grasped by the mind, and that is the reason the Buddha didn’t answer if the cosmos is finite or infinite and why one of the acinteyyas is speculating about (the beginning of the) cosmos.

Thanks for your answer, are you sure everything about infinity can be understood and explained? I am doubting this because when googling the problem I find some very weird stuff about infinity and different and conflicting theories and views, but I am not an expert, that’s why Iam asking again.

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Yes, I agree. I think these subtleties are lost in Buddhist texts later on when they become hyperbolic about past lives, especially when they started thinking about past Buddhas and bodhisattvas and writing Avadana stories about them. The basic focus was on a certain end rather than a certain beginning, but that was to avoid taking a speculative position rather than to make one.


What I don’t really understand is this:
If the Buddha knew that the cosmos is finite, why not just say it? What harm would be done if everyone knew the cosmos is finite?

I believe the reason the Buddha didn’t answer is because the answer cannot be understood by the mind and thinking about it will never lead to understanding it and that’s why it is harmful. Maybe the cosmos is infinite but not in the way we understand it, or neither finite nor infinite.

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Well, there’s a social aspect to the situation at the time. People were arguing about things that can’t be objectively settled. Sure, the Buddha could say, “X is true.” But then non-Buddhists would argue with Buddhists about it if they disagreed. When people argue about issues that can’t be objectively settled, they get angry, they can become hateful, they can harbor animosities for an entire lifetime. All of that nurtures the hindrances rather than ceases them, which then means practitioners have a hard time meditating effectively. Etc. I think this was the main concern.


Thanks, makes sense.

  1. All infinities here has to be limited to countable infinities, not uncountable infinities like the total real numbers between 1 and 0. Countable infinities are like the set of natural numbers to infinity. This is because we can count lifetimes, rebirth and death of sentient beings are countable, it makes no sense to say a person had lived pi lifetimes. Also, a cycle of the universe is countable. Even if humans are homo sapiens only and exist for a short period of time in only some universe cycles, given no beginning, there are enough infinities of humans.

  2. Doesn’t matter the relative frequency an average unenlightened sentient being got reborn into the higher or lower realms. Even with a low chance of being reborn as a human, times that by infinite past, it’s likely that almost everyone had been reborn as humans for infinite times already. Also, keep in mind that the proper doctrine for rebirth is using kamma, not chance. So cause and effects are there. Chance is merely a statistical modelling since we are ignorant of the exact workings of kamma. So what actions an individual does might not be good to use stats to model, as it gives a false impression that an individual’s actions are random, by chance, no reason, etc.

  3. Sutta support for everyone had been reborn as humans before: SN 15.11: Duggatasutta—Bhikkhu Sujato (

SN 15.14: Mātusutta—Bhikkhu Sujato (

The first one seems to indicate that whatever suffering and happiness we see other humans had been through, we too had been in the same position. So generalize this to mean that those who are humans had been humans before. This statement likely applies to all sentient beings as well, to indicate that they too had been humans before.

For not easy to find a being who had not been our mother, father, etc… it limits the realms of rebirth to humans and animals. So at least everyone had been humans and animals before. However, even within the realm of infinities, there’s a clue in the suttas to mean that it’s not an absolute given that all beings must had been at some point in the past be our mother. This gives an indication that just because there’s a non-zero chance of a thing happening even across infinite time, doesn’t mean it had happened already infinite times.

  1. Now as to the path to liberation, one might not want to use chance to think in this manner. Say even if we all had been monks and nuns before, and strove towards enlightenment, there was something or another which made us forget the path, before we entered the path towards stream winning. However, this doesn’t mean that there’s no chance for liberation, as it’s clear that there are people who are liberated. If anything, this message tells us to be vigilant not to miss out this time!

  2. On liberation, we might want to think it in this manner: a person wants to get durians, but he only has mango seeds. So he plant the mango seed, water it, wait for it to mature, etc. Then only mango fruits appear. He reflects that according to quantum mechanics, the atoms and molecules position are in quantum flux, however unlikely it is, there’s a non-zero chance for the DNA of a mango to spontanously rearrange itself to become the durian DNA. So he repeated the process of planting the mango seed to wait until it becomes durian DNA spontaneously. Not just one cell in the Mango seed has to do it, all the cells in the mango seed has to be able to spontaneously transform into Durian DNA. Not other types of fruits too, not grape, orange, apple, etc, only durian counts. So he does the same thing again and again.

Another person goes into the genetic engineering lab, studies the difference between the mango and durian DNA, do the proper procedure of cut and pasting genes, then successfully transformed the mango DNA to durian DNA and still needed some trial and error before they in a very short time was able to get durian from mango.

So too, the path to liberation has it’s causes and conditions. A person who doesn’t cultivate the noble 8fold path doesn’t get liberated. A person who tries to vary their spiritual path blindly might or might not stumble upon the noble 8fold path and become a private Buddha, in a very rare chance occurrence. A person who follows the path laid down by the Buddha is akin to those who go into the genetic engineering lab to plant the best causes and conditions for the results to ripen.

While doing good or bad (which leads to rebirth up and down samsara) is fairly determined by kamma and seems almost impossible to avoid throughout the long stay in samsara for infinite time, there’s nothing intuitive or easy to stumble upon for the kamma which is neither bright nor dark, the noble 8 fold path. Especially right view.

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I think the question is for infinity years that have passed if the probability of unbinding or nibbana is 1 to infinity then logically we should be liberated since infinity years have passed since beginingless time but we are still not liberated even now

May you all be happy :smiling_face_with_three_hearts::smiling_face_with_three_hearts:

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This is a good point that i didn’t mention.

Good way to put it. This is also why there can be no beginning because all birth has to be construed based on previous development [kamma].

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Sharing my thoughts:

If there are infinite past lives, then enlightenment would have happened at least to some before the end of infinity or exactly after crossing infinity if the chance is one to infinity, so it seems it must be impossible.
But for everyone who gets enlightened infinity plus a certsin number of lives have passed. But there is no before infinity because from every single life there are infinite lives before, that were all at some point the present life. So one has crossed infinity without ever being before infinity or being in the process of crossing infinity.
That seems all a bit paradoxical. So maybe the chance is not 1 to infinity in a weird way.

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Now this is just the confusing property of infinity, it breaks logic. There’s no such thing as crossing infinity. Infinity is not a thing. So don’t think of this. I think this is perhaps why the Buddha didn’t want to declare if the universe is eternal or not.

Just think like this: everyone who gets enlightened walks the noble 8 fold path in the present life. Everyone who doesn’t haven’t completely finished walking the noble 8fold path. There’s no guarantee that everyone will walk the noble 8fold path. There’s a chance for us now to do so. Best do so instead of asking who shot the arrow, what’s the poison, what is the arrow made of etc.

Yes, that’s what I meant, it breaks logic.

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I think it is rather because people have a misconception about what is ‘a world’ and he didn’t want to add to their delusion by answering speculative questions in a categorical manner.

There are these passages that i think are relevant;

[When this was said, the Blessed One responded:] “I tell you, friend, that it is not possible by traveling to know or see or reach a far end of the cosmos [loka] where one does not take birth, age, die, pass away, or reappear. But at the same time, I tell you that there is no making an end of suffering & stress without reaching the end of the cosmos. Yet it is just within this fathom-long body, with its perception & intellect, that I declare that there is the cosmos, the origination of the cosmos, the cessation of the cosmos, and the path of practice leading to the cessation of the cosmos.”

It’s not to be reached by traveling,
the end of the cosmos —
And it’s not without reaching
the end of the cosmos
that there is release
from suffering & stress.

So, truly, the wise one,
an expert with regard to the cosmos,
a knower of the end of the cosmos,
having fulfilled the holy life,
knowing the cosmos’ end,
doesn’t long for this cosmos
or for any other. An4.45

World is defined here;

That in the world by which one is a perceiver of the world, a conceiver of the world—this is called the world in the Noble One’s Discipline. And what, friends, is that in the world by which one is a perceiver of the world, a conceiver of the world? The eye is that in the world by which one is a perceiver of the world, a conceiver of the world . The ear … The nose … The tongue … The body … The mind is that in the world by which one is a perceiver of the world, a conceiver of the world. That in the world by which one is a perceiver of the world, a conceiver of the world—this is called the world in the Noble One’s Discipline. Sn35.11

I think this goes with Sabba Sutta

The Blessed One said, “What is the All? Simply the eye & forms, ear & sounds, nose & aromas, tongue & flavors, body & tactile sensations, intellect & ideas. This, monks, is called the All. [1] Anyone who would say, ‘Repudiating this All, I will describe another,’ if questioned on what exactly might be the grounds for his statement, would be unable to explain, and furthermore, would be put to grief. Why? Because it lies beyond range.”

I think that they speak about taking another birth as ‘next world’

And what is the right view with effluents, siding with merit, resulting in acquisitions? 'There is what is given, what is offered, what is sacrificed. There are fruits & results of good & bad actions. There is this world & the next world. Mn117

Finally there is that ayatana associated with a cessation of the world;

There is that dimension, monks, where there is neither earth, nor water, nor fire, nor wind; neither dimension of the infinitude of space, nor dimension of the infinitude of consciousness, nor dimension of nothingness, nor dimension of neither perception nor non-perception; neither this world, nor the next world, nor sun, nor moon. And there, I say, there is neither coming, nor going, nor staying; neither passing away nor arising: unestablished,unevolving, without support. This, just this, is the end of stress. Ud8.1