The Infinity Problem in Buddhism

July 15, 2017; Revised February 5, 2018 (link at the end of the post)

This question was posed to me by Mr. C. Saket from India, who also sent along his ideas too. Apparently, this question has been discussed in several online forums, without reaching a satisfactory answer.

1. The question is: “The Buddha has said that there is no discernible beginning to the rebirth process (see the suttas in Anamatagga Saṃyutta, Samyutta Nikaya). In other words, we have had infinite number of attempts at attaining Nibbāna. So, why have we not attained Nibbāna yet?”

  • This question seems to have its origin in the infinite monkey theorem, which states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare.
  • By the way, this infinite monkey theorem is another evidence of how unimaginably large infinity is: “Infinity – How Big Is It?“.

2. First of all, the proof of the monkey theorem is based on a monkey generating random characters using a keyboard. The following example is given in the above link to the monkey theorem:

  • Suppose the typewriter has 50 keys, and the word to be typed is banana. If the keys are pressed randomly and independently, it means that each key has an equal chance of being pressed. Then, the chance that the first letter typed is ‘b’ is 1/50, and the chance that the second letter typed is a is also 1/50, and so on. Therefore, the chance of the first six letters spelling banana is
(1/50) × (1/50) × (1/50) × (1/50) × (1/50) × (1/50) = (1/50)6 = 1/15 625 000 000 ,

less than one in 15 billion, but not zero, hence a possible outcome.

  • Let us first discuss the differences between the infinite monkey theorem and the current problem. However, at the end it will be shown that the conclusion of the infinite monkey theorem does apply to the present case too, and there is no contradiction even though infinite number of beings have not yet attained Nibbana.
  • The key point is that an infinite number of beings have attained Nibbana. This is why infinity is such a complex concept.

3. Attaining Nibbāna is NOT a random process. First of all, one needs to hear or read about the Tilakkhana (anicca, dukkha, anatta) in order to even start on the process.

  • No matter how hard one tries, one will never be able to attain Nibbāna if one has not heard the TRUE VERSION of the Tilakkhana. In some aeons (maha kalpa, lasting roughly 10 billions years), there is not even a single Buddha, and the probability of attaining Nibbāna during that aeon is ZERO.
  • Even during a given Buddha Sāsana, the true meanings of the Tilakkhana get distorted from time to time and thus the probability goes to zero. For example, at present time, most people interpret anicca as impermanent and anatta as “no-self”.

4.  There have been only 7 Buddhas within the past 91 maha kalpas. This timeline is discussed in the “Mahapadana Sutta (DN 14)“.

  • There was only a single Buddha (Vipassi) in the maha kalpa that was 91 maha kalpa earlier. There were no Buddhas in the next 60 maha kalpas,  and then two Buddhas (Siki and Vessabhu) appeared. Then there were 30 maha kalpas without a single Buddha, and so far in the current maha kalpa there have been four Buddhas (Kakusanda, Konagama, Kassapa, Gotama), and one more Buddha (Maithree) is expected to appear before this aeon ends.
  • Even during a given Buddha Sāsana, only a fraction of HUMANS will get to hear/read about the true Tilakkhana. Today, the percentage of Buddhists worldwide is roughly 5%-10%, and much less than 1% have heard about the true Tilakkhana.
  • Furthermore, the human population is negligible compared to the population of beings in the apāyas, who have zero probability of comprehending Tilakkhana. So, we can see that there are many zero probabilities for a given LIVING BEING, compared to a relatively few non-zero probabilities.

5. We can refine the progress to Nibbāna a bit more. The key to Nibbāna is first to attain the Sōtapanna stage; once that is reached, Arahanthood is guaranteed. It is mostly only in the human realm that one will be able to attain the Sōtapanna stage.

  • In order to attain the Sōtapanna stage, one first needs get rid of the 10 types of miccā ditthi; see, “Miccā Ditthi, Gandhabba, and Sōtapanna Stage“. Only then one will be able to comprehend the Tilakkhana and start on the Noble Eightfold Path to attain the Sōtapanna stage.
  • Suppose one is born human during the time of a Buddha, having gotten rid of the 10 types of miccā ditthi, makes good progress towards the Sōtapanna stage. But if, for some reason, he/she is unable to reach the Sōtapanna stage (i.e., without grasping Tilakkhana) and dies, then even if the next birth is in the human realm, one could be born to a family with miccā ditthi and thus may have to start over.
  • We do carry our “gathi” from life-to-life. “Good gathi” can grow in the next life under conducive conditions, but they can also be reversed or changed under adverse conditions.
  • We can call such an occurrence an “event with significant probability”.

6. Therefore, reaching Nibbāna cannot be considered a mechanical process, and thus cannot be compared to a monkey hitting arbitrary keys on a keyboard to generate Shakespeare’s Hamlet.

  • One has to make a concerted effort — via several intermediate stages — to reach Nibbāna.
  • However, a mathematician could still say that one could consider an infinite number of such “events with significant probability” by a living being per #5 above.
  • One such “event with significant probability” can be equated to a monkey hitting a key stroke on the keyboard. 
  • Even though such “events with significant probability” may be separated by huge time spans, given infinite time, an infinite number of them can accumulate. Therefore, the infinite monkey theorem should still hold.

7. It is indeed true that an infinite number of living beings HAVE ATTAINED Nibbāna in the past.

  • Not only that, infinite number of living beings have attained the Buddhahood in the past. Of course, attaining the Buddhahood is infinitely more difficult than attaining Arahanthood.
  • Therefore, the infinite set of living beings who have attained Nibbāna is “much larger” than the infinite set of living beings who have attained the Buddhahood.

8. Infinity is a very complex concept. There are many levels of infinity. Infinity minus infinity is still infinity. So, even as there have been an infinite number of Buddhas, and and even higher infinity of those who attained the Arahanthood, there are still an infinite number of living beings (including us) who have not yet attained Nibbāna.

  • Therefore, while the infinite monkey theorem does apply here, there is no contradiction.
  • Of course, several other questions now arise: Where do all these infinite number of living beings live? Do they all live in our Solar system? Have all these infinite number of Buddhas appeared in our Solar system? It will take many more future posts to fully explain these, but we can summarize as follows.

9. There are 31 realms that are associated with our Earth or the Solar system (Cakkāvāta or  Cakrāvāta), see, “The Grand Unified Theory of Dhamma – Introduction“. So, there are many more living beings in our Cakkāvāta other than the humans and animals that we can actually see; most living beings are in the other three realms of the apāyas; animal realm is the fourth.

  • Furthermore, there are an infinite number of such Cakkāvāta (planetary systems) in existence at all times with living beings. Buddhas can appear in some of them.
  • These Cakkāvāta are in clusters of small, medium, and large “world systems” (galaxies, galaxy clusters, and superclusters in terms of modern science). But none is permanent. They come into being and eventually perish, only to reborn again. Just like us, these world systems also undergo death and rebirth; it is a cyclic process. We will discuss this at a later time.
  • Within the past 100 years or so, scientists have confirmed the existence of billions of planetary systems within each galaxy and billions of such galaxies in our universe. As far as science is concerned, the number of  Cakkāvāta (planetary systems) is likely to be infinite — as stated by the Buddha 2500 years ago.

10. If there are infinite number of planetary systems with life (just like ours), how come that scientists have not detected life outside our Solar system?

  • The distance between adjacent  Cakkāvāta is enormous. The star closest to us, Proxima Centauri, is 4.2 light years away from us. This means, if we travel at the speed of light (186,000 miles/second), it will take 4.2 years to get there! Of course, we can only travel at a small fraction of the speed of light.
  • For comparison, our own Sun is only 8 “light minutes” away from the Earth, i.e., it takes only 8 minutes to get to the Sun if we travel at the speed of light. The moon is about 1.3 light-seconds away from the Earth (240,000 miles). We have been able to only land on the Moon so far!
  • So, it is fair to say that we may not be able to communicate with living beings in another planetary system in the near future, if ever. Even if we find that our closest star has a habitable planet like Earth, it will take over 8 years to even send a light signal and get a reply back.

11. This is why the Buddha said not to waste time on thinking about these questions. In the Acinteyya Sutta (AN 4.77), he listed four things that are inconceivable (acinteyya) by a human, and if one persists on that path one may become insane (may lose one’s mind, because these issues are so complex):

  • Buddha Visaya (things that are discernible to a Buddha), Jhana Visaya (powers that can be accessed by one in jhānās), Kamma Vipāka (how the laws of kamma work), and Loka Cintā (comprehending the real nature of the world).
  • The issue that we just discussed belongs to the fourth category. We will never be able to figure out or comprehend everything about the unimaginably large and complex world (the universe). But from the above discussion, hopefully we all can at least get a glimpse of the complexity of the universe with infinite number of Cakkāvāta like ours.

February 5, 2018: An update on this subject can be found at the Discussion Forum topic, “The Infinity problem – BIG Doubt“.

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