Revised June 3, 2018; January 19, 2020; August 9, 2021; September 23, 2022
Infinity is a concept that is hard to comprehend. The rebirth process (or Samsāra) does not have a traceable beginning, i.e., it extends back to infinity. Mathematicians have concluded that there are many levels of infinity!
Introduction
1. What is the biggest number you can think of? Well, add one, and you will have a lbigger number! There are some large numbers that we are aware of. With record budget deficits of the developed nations in trillions of dollars (and the total nominal value of all the derivatives traded around the world approaching a thousand trillion dollars, or a quadrillion dollars), trillion and quadrillions are indeed large numbers.
- Even though a trillion rolls off the tongue, not very different from a billion, a trillion is much bigger than a billion. Spending a billion dollars a day will take a thousand days to spend a trillion dollars.
How to Represent Large Numbers?
2. The number of molecules in a cubic centimeter of gas is 2.7 x 1018 or 2.7 x 10^18 (this is a simple way to express big numbers; instead of 10000, we write 104 or 10^4). Since electrons are even smaller, you would think there would be a humongous number of electrons in the observable universe; the estimated number is around 1087. That is, of course, a huge number, but it is not infinity by any means.
- That should give you an idea of the power of an exponent. Each time the exponent increases by one, the number becomes ten times bigger. So, even though 1087 may not look that big compared to 1018, it is a humongous increase. Another large number should be the distance from the Earth to the edge of the observable universe, estimated to be about 46 billion light-years or around 1023 miles. Even though such large numbers are hard to be contemplated in our minds, they are all finite.
What Is a Googol?
3. There are some famous large numbers. A Googol is 10100, which is unimaginably vast compared to even the number of electrons in the universe (1087). As an aside, the internet company Google was to be named Googol, but someone made a mistake, and Google was the name given. A Googolplex is a whopper; it is 10Googol or 10(10^100). There are many such “famous large numbers.”
- Yet, you can add one to any of these large numbers and always get a bigger number. Therefore, no number, however large, is still finite.
Infinity – Beyond Any Conceivable Number
4. So, the mathematicians coined the term “infinity” to denote an indefinitely high number; The word comes from the Latin “infinitas” or “unboundedness.” Since infinity is uncountable, it has some strange characteristics: whatever you add to (or multiply by) an infinity (even if it is another infinity), you still end up with infinity.
- The famous German mathematician David Hilbert illustrated the “abnormal” properties associated with infinity using the idea of an “infinity hotel,” which has an infinite number of rooms. The “infinity hotel” always has a vacancy: the management can always ask the person occupying the Nth room to move to the (N+1)th room, (N+1)th room to move to the (N+2)th room, and so on, and thus give the Nth room to the new guest. Even if an infinite number of new guests arrive, the hotel can accommodate all of them!
Infinity Is Real
5. That is not to say that infinity is a useless or bogus concept. The arguments described above are valid. Mathematicians cannot do many integrations without infinity. Physicists deal with infinity all the time (but they try to end up with finite physical values).
- The concept of infinity is real (and weird). For example, a line of any finite length has infinite points, whether it is an inch or thousand miles. The invention of calculus by Newton and Leibniz helped handle some problems arising from such situations.
Space and Time – Infinite!
6. In the physical sense, infinity is a rather vague concept meaning “larger than anything that could in principle be encompassed by experience.” For example, space is infinite, and as far as our sophisticated instruments allow us to “see,” there is no end.
- Our universe is possibly spatially infinite since scientists can “see” only to a finite extent. So, space is unlimited.
- What about the time? If our universe started at the Big Bang, that inflationary theory says multiple parallel universes exist.
- According to the “cyclic theory” model, an alternate theory, the same universe comes to a “Big Crunch,” which leads to another Big Bang, and the whole process keeps repeating. So, there is no beginning to time either; time is infinite.
- By the way, both those theories are not correct, according to Buddha Dhamma. Individual star systems (“Cakkāvāla” or”Cakkāvāta“) undergo the birth-destruction cyclic process.
- I will write more in the future, but see the discussion: “Multiverse: Different Physical Laws and Different Dhamma?“. The lifetime of a Cakkāvāta (like our Solar system) is called a Mahā Kappa (great eon) in Buddha Dhamma.
Samsāra (Rebirth Process) Goes Back Infinite Time!
7. The Buddha used a great eon as the measurement unit to help his followers visualize the enormous length of samsāra. A great eon (mahā kappa or mahā kappa) is said by the Buddha to be longer than the time it would take a man to wear away a mountain of solid granite one yojana (about 7 miles) around and one yojana high by stroking it once every hundred years with a silk cloth.
- These days scientists use the word “eon” to denote the duration of a universe (from the “big bang” either to a “big crunch” or just fading away). But a Mahā Kappa means the lifetime of our Solar system. Our universe has “no beginning.” I believe that in the future, science will conclude that the “Big Bang Theory” is not correct (which says that our universe came into existence from nowhere in a “Big Bang.”) See the discussion: “Multiverse: Different Physical Laws and Different Dhamma?“.
Another Analogy of the Buddha
8. One day, the Bhikkhus asked the Buddha how many “great eons” had already passed and gone by. The Buddha told them, “Suppose, Bhikkhus, there were four disciples here, each with a lifespan of hundred years, and each day they were each to recollect a hundred thousand great eons. There would still be great eons not yet recollected by them when those four disciples pass away at the end of a hundred years. Because, Bhikkhus, this samsāra is without discoverable beginning”.
- A fascinating book about such hard-to-grasp ideas (in science) involving infinity is “The Beginning of Infinity: Explanations That Transform the World” by David Deutsch.
- Infinity is a mind-boggling concept. For example, one question that comes up frequently is the following. We have had infinite time to attain Nibbāna. So, why have all living beings not attained Nibbāna yet?”
- I have discussed that in “The Infinity Problem in Buddhism.”
Summary
9. We (including all living beings today) have “lived” for an infinite time. There is no traceable beginning to life, per Buddha. See “Origin of Life – There is No Traceable Origin.”
- We suffered much more than any brief stretches of pleasure during much of that time. That is because births in “good realms” (like human, Deva, and Brahma realms) are rare. See “How the Buddha Described the Chance of Rebirth in the Human Realm.”
- Most of our past births had been in the four lower realms (including the animal realm), where suffering dominates.
- That is why the Buddha admonished us to strive to attain Nibbāna to avoid such harsh suffering in future rebirths.
Detailed discussion in the subsection, “Origin of Life.”
