Can Infinity Have an End?

[Mr. SmartyPants]

Today in the lunchline at school, some guy I know came up to me, his name is Tom, who was a Buddhist or some wannabe Buddhist. Anyway I asked him a question, and the conversation went something like this:

Me: "You believe that Buddha had infinate reincarnations correct?"
Tom: "Yeah"
Me: "You believe that Buddha also had a final reincarnation correct?"
Tom: "Yeah"
Me: "If he had a final reincarnation, then how dd he have infinate reincarnations? Those are two contradictory statements"

He told me that an infinate value did not have to have a unreal end and an unreal beginning. However the end value could be real (a final reincarnation) and there could be no beginning, and that would still be considered infinity.

In laymens terms, infinity can have an end but no beginning. Likewise Infinity can also have no end but have a beginning.

So my first question is: Did Buddha ever claim to have a first reincarnation?

Second: Can Infinity have an end that is a real value? (Assuming that the beginning is unreal)

[SManBeyond]

Hola MSP...it's been a while...

I don't claim to know a lot about Buddhism, but I did study its origins in some detail. Here are my answers to your questions based off of the knowledge I had:

1) Buddha never claimed to have a first incarnation. Buddhism would say that the universe had no real beginning. Since people live in the universe, no person has had a "beginning". So Buddha would have said that he had no beginning, so he never claimed to have a "first" incarnation...he would say that he has existed forever.

2) To be honest, I'm not sure if I understand your question, but let me take a stab at it.

One way of thinking of infinity is starting at a number (like 0), and then adding 1 (0+1 =1, then adding 1 again (to give 2), and keep adding 1 over and over again forever. So in essence, 0 is your starting point and there is no endpoint.

Your question is: Is it possible for infinity to have no starting point, but an "endpoint" (i.e. stops at a certain value)? The answer is yes. Here's what you do:

Take some number (like 1). Subtract 1. (You now have 0). Subtract 1 again. (You now have -1). Subtract 1 again (You now have -2). Keep subtracting 1 over and over again, and you hit what's called negative infinity. It's like infinity, but it's constantly getting smaller instead of constantly getting bigger.

Let me know if this helps. If not, I'll try again or defer to an expert.

[Scribs]

Your question is: Is it possible for infinity to have no starting point, but an "endpoint" (i.e. stops at a certain value)? The answer is yes. Here's what you do:

Take some number (like 1). Subtract 1. (You now have 0). Subtract 1 again. (You now have -1). Subtract 1 again (You now have -2). Keep subtracting 1 over and over again, and you hit what's called negative infinity. It's like infinity, but it's constantly getting smaller instead of constantly getting bigger.

Let me know if this helps. If not, I'll try again or defer to an expert.

Ah, but if that is infinity, then if you have an infinite ammount going back from one point, it could not be infinite because there would be an ammount bigger. That ammount would be an ammont that had infinite numbers both before and after the point. This infinity would be twice as large as the first infinity.

[Heart of Sword]

Infinity is infinity. It can't have an end; that would go against the entire idea of infinity. It would be like saying, "can blue be red?" or "can a rat be a giraffe?" It's impossible.

[Sammy Boy]

I agree with Heart of Sword.

The very definition of inifity seems to rule out something with a beginning but no end (that's "semi-infinite").

I think to talk about infinity outside of its normative definition is like trying to describe a round square.

[Heart of Sword]

Right.

"It would be a square, if it weren't round."

If it had an end, it just wouldn't be infinity anymore. It would be "a long time."

[Technomancer]

Second: Can Infinity have an end that is a real value? (Assuming that the beginning is unreal)

Yes, as has been pointed out, the real number line is just such a case e.g. (-Inf,0], and infinities that start and have no end can also be represented. In addition, it is also possible to have an infinte surface that is bounded.

[Heart of Sword]

*hides* I hate deep responses...it makes my brain...make owies...

Anyway...Technomancer? I don't get it...

[SManBeyond]

Thank you Technomancer.

And to clarify to the people above, you can define infinity as constantly getting bigger. However, you can also define infinity as constantly decreasing (i.e. always getting smaller). Think of it as the opposite of getting bigger...it's still infinity though (just backwards).

Now let's see how confusing that explanation is.

[Heart of Sword]

But infinity is infinite....

This is too much for my small brain....*sweatmark*

[Sammy Boy]

SManBeyond and Technomancer - just wondering if the infinity you guys are talking about is more of a mathematical one than a philosophical one?

[Peanut]

SManBeyond and Technomancer - just wondering if the infinity you guys are talking about is more of a mathematical one than a philosophical one?

I don't think there is actually a difference between the mathematical concept and the philisophical one, both negative infinity and positive infinity are infinite, so how is it any different from a philisophical infinity. If you wan a non-mathematical example think of God and our souls. God is pretty self explanatory, and our souls have a definite starting point and continue on through this life and into eternity.

[Puritan]

Infinite is usually more of a concept than a number. For a real brain twister, realize that some infinities are larger than others. In fact, a few years ago I remember proving in math class that an algebraic equation that was equal to infinity divided by another equation equal to infinity resolved into a rational answer.

As for eternity, and reincarnations, if I recall correctly the Buddists believe (similarly to the Hindus) that everything comes from and returns to a pan-theistic god. Thus, the logical inconsistancies could work themselves out with budda having a final incarnation as himself, returning to the universe, and just merging back in as an undistinguished entity.

Hope that made sense.

[SManBeyond]

As for eternity, and reincarnations, if I recall correctly the Buddists believe (similarly to the Hindus) that everything comes from and returns to a pan-theistic god. Thus, the logical inconsistancies could work themselves out with budda having a final incarnation as himself, returning to the universe, and just merging back in as an undistinguished entity.

Actually that may stem from a later school of Buddhism. There were three forms of thought that were taught in the early days before Buddhism left India and went all over to Asia...each of them taught that the universe did not stem from anything. It had just always existed, and trying to solve where it came from was thus pointless.

Gods existed, but they weren't like the God of the Bible from which all beauty and creation stems. They were more like the Greek gods who had limited control in the world. Even they were below Buddha and arhats (Buddhist saints) in the spiritual hierarchy.

All that to say that in the early days of Buddhism, that wasn't what was taught.

[CDLviking]

To grasp infinity with an end, just think of a ray in geometry. It has a starting point, but travels on in one direction to infinity. You do this kind of thing all the time in highschool math classes. Our own souls are much the same. We have a starting point but will live on for eternity with God (hopefully, ) in a life without end. God, however, is the only existence that exists infinitely in both directions (well to be technical, he exists outside of time, but that doesn't help illustrate the point).

The problem with infinite reincarnations traveling backwards is one of infinite regress which can only be solved in the way that Puritan suggested by retreating to a pan-theistic origin. That begs the question, why stop?

[Felix]

*head swims* Oh boy.

From what I can see, using the number concept, you say that a number could start at zero, and go on to infinity, or do the same thing backwards, and that makes a certain degree of sense as far as numbers are concerned, but I don't think infinity as it applies to life can actually have an end. There can be a point in infinity (EG: a point on a geometric line) that can perhaps divide the line into two rays. But that wouldn't truly be ending the infinity of the line, it would only be creating two different infinities: One that travels back from the point on the line, and one that travels foward.
There is truly only one infinity, God's infinity. When we're born, we make our own point on the infnity line, the point where our infinity ray starts. So in appliance to ourselves, there is a sort of beginning to infinity, but that's really just where we come in. Infinity (God) has been there all along. Does that make any sense? It makes sense to me o.O

<-----------------------*----------------------------------->

So that line is infinity, the infinity that has always been there. The infinity God has always lived in, and the infinity we live in now. That dot is our starting point. (When the world was born, or when we were born) and so you see there is the infinity that's behind us, the infinity that was there before, which is the same infinity that we live in now. It stretches on forever in front of us. So OUR infinities would have a real starting point, but infinity is still infinity, and we're only living in one.

Edit: I noticed that I'm basically restating the point CDLviking made. Oh, I said point. Ahahaha. *ahem* Sorry.

[Ingemar]

That begs the question, why stop?

Laziness or the fear that Christians or Muslims are right? LOL

Puritan is right about some infinities being "larger" than others. If you think about integers (i.e., 1, 2, 3, any number that is not a mixed number or has only 0 as a decimal place), they extend into infinity. However, if you count all the "numbers" between 0 and 1, 1 and 2, basically any two integers, you find that the the space between those two can be divided up infinitely (this is strictly a theoretical rather than physical concept, because unless you are some kind of physicist, you accept that matter can only be divided so far (hence, atom comes from the Greek "cannot be split")).

It is also possible to sum an infinite number of segments and come up with a finite value. This is the entire basis of calculus.

[Puritan]

I think you misunderstood me, SManBeyond. Pantheism doesn't actually involve a god, it involves the entire universe being god and god being everything. Thus, the whole universe always was thing came about. You may have some semi-differentiated "gods" (think shiva or krishna from Hinduism), but they all actually belong to a great pantheistic "god," which consists of everything. You're saying the same thing I am, it's just that I'm using different words.

I would postulate that God has not always existed in the infinity we exist in, He created it. As the one self-existant being (i.e. His existance relies upon Himself) He alone existed intially. God is timelessly eternal, time itself is a creation. How's that for a mind-bending idea?

[Slater]

There is a difference between infinity and endlessness. Infinity involves something that has no beginning nor an end. In mathematical terms, it is an image that exists at a point or number of points that one can get arbitrarily close to, but never reach.

Endlessness is something that has a beginning but no end. This is what our lives are like. While our souls had a beginning, they will never reach an end; such is one of the promises of God.

[termyt]

(hence, atom comes from the Greek "cannot be split")).

Of course, atoms can be split...
I mention that because we humans still only have a very small understanding of the universe. Our knowledge covers vast libraries full of volumes of knowledge, but it is an infinitesimal amount compared to the true nature of the universe.

If we look at the meaning of the word infinity, we find it comes from the Latin meaning “no end.â€

[Arnobius]

I would postulate that God has not always existed in the infinity we exist in, He created it. As the one self-existant being (i.e. His existance relies upon Himself) He alone existed intially. God is timelessly eternal, time itself is a creation. How's that for a mind-bending idea?

I don't think it is too hard to conceive, though as you get into specifics you can get a headache. God always IS. Time began when he created the universe. Time will end when the universe does. But God will continue to be when the universe is done. He exists outside of time.

Humans have been created with a mortal body but an immortal soul by God.

So to borrow from CDLViking's geometry analogy, we could say (simplifying):

• God would be symbolized by a line, with no beginning or end.
• Humans are a ray. A fixed beginning and no ending (considering the soul is immortal). We were created within time, but our soul will continue outside of time once we die and face judgement
• The Universe is a line segment with both a beginning and end

We will live on because God is outside of time and outside of the universe and our souls will continue to exist outside of time. I think eternity in this case is easier to understand.

Of course it does not explain what it will be like to be eternally with God or eternally seperated from Him... for that we need the Bible, not mathematical philosophy

[mitsuki lover]

MSP,is your friend into Zen?It kind of sounds like those were Zenlike statements.
Any way from what little I understand Buddhism,and can we really understand a totally non-Western religion like it?,Buddha is simply an overall term for anyone who has gained total Enlightenment.The man who we know has THE Buddha was just one of many who through several incarnations first became a boddhivista,Buddha to be, and then in his final incarnation a Buddha or Enlighented One(sorry spelling).It gets even more confusing if you try to read some of the Buddhist literature.At a Friends of the Library book sale I once bought a Penguin edition of an anthology of some Buddhist classics.I read the first part and it really was confusing.According to it the Gods themselves had to be converted to Buddhism,and to do so Buddha had to go to the heavens and preach to them.
No,I did not make that up,that is what I read.
As far as infinity goes,if it can end than IMO it can't be infinite.

[Mr. SmartyPants]

MSP,is your friend into Zen?

Yes, he is definately into Zen

[uc pseudonym]

Having read all the responses to this thread, I have one question regarding many of them. I would argue that infinity has distinct theoretical and mathematical concepts.

Unless I am mistaken, under the mathematical definition, only a value can be infinite, not an object itself. For example, a square that is one unit by one unit contains an infinite number of points. A square that is 2x2 also has an infinite number of points. Neither square is infinite, merely the number of points within it. Subtracting the former from the latter still gives us 3 square units.

What, therefore, does it mean to say that God is infinite? While we can't describe God with human words, I think we do a much better job with different definitions. Then again, I could be misinterpreting previous comments.

Of course, all of this has somewhat gotten away from the original question.

[EricTheFred]

Can infinity have an end?

Not a meaningful question. Geometrically, Infinity IS an end. Arithmetically,
Infinity is a number. So supply a different number and ask the question again.
Example: "Can four have an end?"

[Puritan]

Infinite:
1 : extending indefinitely : ENDLESS <infinite space>
2 : immeasurably or inconceivably great or extensive : INEXHAUSTIBLE <infinite patience>
3 : subject to no limitation or external determination
4 a : extending beyond, lying beyond, or being greater than any preassigned finite value however large <infinite number of positive numbers> b : extending to infinity <infinite plane surface> c : characterized by an infinite number of elements or terms <an infinite set> <an infinite series>

Infinity
1 a : the quality of being infinite b : unlimited extent of time, space, or quantity : BOUNDLESSNESS

(From the Merriam-Webster Online Dictionary, http://www.m-w.com)

Thus, I think that is is meaningful to say God is infinite, He is "immeasurably or inconceivably great or extensive," and "subject to no limitation or external determination." Within human reason, I think that's a great start for discussing God. I also think the question of infinity having an end is also meaningful, but has a set answer. By definition, no. I think part of the problem is that infinity refers to a mathematical concept and a logical concept, and we can get them mixed up. As God is not mathematical, I was thinking on the logical grounds, not mathematical ones.

[Mr. SmartyPants]

My real question is if statement A: Buddha (Siddhartha) had infiniate reincarnations, and B: Buddha (Siddhartha) had a final reincarnation, contradictory statements or not. I'm not really trying to ask for infinity in other definitions.

[SnoringFrog]

Well, I would have to say I think that it could. Although the concept of having on infinity that is greater than anohter is addling, it does make a bit of sense. I'm with the idea that infinity could be soemthing that never begins and never ends, soemthing that begins and never ends, or something that never begins but ends.

I also think that the idea Felix posted sounds thesible as well, especially when I consider it along with those that mentioned infinities being different lengths. Time, the universe, our souls, and everythin else all have their beginnigs on God's infinity, and our souls would have an infinity within that one.

EDIT: Hard to say, I suppose it would depend on how one appraoched it. If the infinite reincarnations never had a beginning and had an end, then no, those statements are not contradictory, IMO. However, the way it sounds to me, the reincarnations did have a beginning, which would be when Siddhartha had his first reincarnation, and then they had an ending, when he had his final one; when you look at it that way, they do seem contradictory, because something with a beginning and an end could not be defined as infinite.

[Puritan]

As I mentioned above, I think this is solved by the Buddhist concept of the universe. Everything is God, God is everything. In Bhuddist belief, Buddha as Buddha may have had an infinite number of incarnations because the universe had no ending and no beginning. Buddha then rejoined the universe after the process of enlightenment, and has had no more incarnations. The basic concept is quite strange unless one believes that the universe has always been, in which case Buddha had an infinite number of incarnations before his final incarnation. I think this ties into the number line argument. If you look at history backwards from the Buddhist perspective, you would see an infinite string of incarnations of Buddha stretching into the past, but that string ended with his final incarnation.

Keep in mind, I think that this is an illogical and wrong way of viewing the world, the universe as we see it just doesn't seem to mesh with this idea. However, if you allow the postulation the the universe always was and will always be, his statements aren't necessarily contradictory.

[CDLviking]

So to borrow from CDLViking's geometry analogy, we could say (simplifying):

• God would be symbolized by a line, with no beginning or end.
• Humans are a ray. A fixed beginning and no ending (considering the soul is immortal). We were created within time, but our soul will continue outside of time once we die and face judgement
• The Universe is a line segment with both a beginning and end

How are we using the term "Universe?" According to thomistic metaphysics the universe is everything except God. In this case the universe will continue to exist as long angels/ourselves/other things exist.

What, therefore, does it mean to say that God is infinite? While we can't describe God with human words, I think we do a much better job with different definitions. Then again, I could be misinterpreting previous comments.

It is easier to talk about what God is not than what he is. To say that go is infinite is to say that he lacks limits.