Can Infinity Have an End?

[Arnobius]

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.

OK... i was thinking of the physical universe of the material world, but thanks for reminding me that I didn't define my terms

[Mr. SmartyPants]

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.

I guess then addressing the laws of thermodynamics to a buddhist wouldn't work?

[Technomancer]

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.

There are other ways of approaching the problem though. The best known one is the use of certain types of projections that can compress infintely long objects to finite ones. Conformal mapping of this sort is sometimes a helpful way of solving some mathematical problems. It's usually covered in a course on functions of a complex variable. Something similar seems to be the case for hyperbolic maps which M.C. Escher sometimes used to represent infinite objects within circles.
http://www.sciencenews.org/articles/20030830/mathtrek.asp

Another possibility is to consider a bounded fractal curve. In a true mathematical fractal, there are infinitely many self-similar scale levels. This (in theory) creates an infinte length/surface that is also bounded.

[uc pseudonym]

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.

I think the general consensus is that if there was no beginning of time, the statements are not necessarily contradictory. But we're having fun with all the tangents...

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.

And I agree. I was merely saying that we need to be clear which definitions of infinity apply to God in this discussion.

There are other ways of approaching the problem though. The best known one is the use of certain types of projections that can compress infintely long objects to finite ones. Conformal mapping of this sort is sometimes a helpful way of solving some mathematical problems. It's usually covered in a course on functions of a complex variable. Something similar seems to be the case for hyperbolic maps which M.C. Escher sometimes used to represent infinite objects within circles.
http://www.sciencenews.org/articles...30/mathtrek.asp

Another possibility is to consider a bounded fractal curve. In a true mathematical fractal, there are infinitely many self-similar scale levels. This (in theory) creates an infinte length/surface that is also bounded.

Interesting. I'm not qualified enough to offer a complete response.

[TurkishMonky]

infinity is NOT a value, it is a definition of somthing that extends forever in a specific direction. so a vector indicationg "lifespan" could theoretically have a specific point and extend infinately into the past. additionally, an infinite vector could start at a specific point and extend infinately into the future (such as our lives will)

so therefore buddha technically could have had infinate reincarnations and have a final reincarnation scientifically.

(fun fun fun tangents!)

thus said, i don't believe buddha is infinate by any means, except infinately msguided....

[Midori]

There's a way in which infinity is just as tangible as zero.

[RefractedAhav]

There's a way in which infinity is just as tangible as zero.

how so?

[Mr. SmartyPants]

I think the general consensus is that if there was no beginning of time, the statements are not necessarily contradictory. But we're having fun with all the tangents...

I do recall ravi zacharias bringing this subject up in one of his books. His reasoning I do not remember, because I lent the book to a teacher in school >_> I really need that back now

[termyt]

There's a way in which infinity is just as tangible as zero.

That's certainly true. Zero itself is an abstract mathematical concept. Mathematics as we know it didn't take off until the zero concept was invented.

Don't believe me? Then, what's the roman numeral for zero? They didn't have one.

So, I postulate that zero is not very tangible. If you disagree, show me by posting a list of everything you have exactly zero of.

[uc pseudonym]

I believe I understand your point, termyt, but I'm not sure what you intend to accomplish by the last statement. It would be easy for me to create a list of things I have exactly zero of: televisions, guns, bathrobes... am I misunderstanding you?

infinity is NOT a value, it is a definition of somthing that extends forever in a specific direction. so a vector indicationg "lifespan" could theoretically have a specific point and extend infinately into the past. additionally, an infinite vector could start at a specific point and extend infinately into the future (such as our lives will)

I'm not sure if you are actually addressing me with this, but I'll respond to clarify. While I said that a value can be infinite, it is obvious that infinity is not a value. What I meant is that "infinity" is a quality that only a value can have under the mathematical definition. By extension, I argued that there are definitions other than the mathematical one.

[termyt]

I believe I understand your point, termyt, but I'm not sure what you intend to accomplish by the last statement. It would be easy for me to create a list of things I have exactly zero of: televisions, guns, bathrobes... am I misunderstanding you?

I doubt you are misunderstanding me except for one part of your post. I don't think it would be easy at all. You listed three things you do not have. How many more things exist that you do not have? There is nearly an infinite amount of things you could have, meaning the list things you don't will be near infinite as well.

[uc pseudonym]

Ah, I see, I did misunderstand you, or rather missed the point. Of course there are a nearly infinite number of things that one could or could not possess, and now that I understand you wanted to draw attention to the ease of the listing it makes more sense.

[mitsuki lover]

Actually I would like to make a theological,if I might,point here,and say that if infinite isn't as infinite as believed than the Universalist claim that the suffering in
Hell is only Age-long and not Eternal would have to be considered.

[uc pseudonym]

That's certainly another twist. I'd like to remind everyone that the issue of Hell will probably get denominational, so consider your posts carefully before sending them.

In any case, I think most of us could agree that if souls always have a beginning point (probably general Christian doctrine), then to classify any period of time for a given soul as infinite would require the non-existance of an end point. It also seems fairly clear that "infinite" is only being used in terms of an amount of time in this setting.

[termyt]

Remember that "infinite" and "eternal" are different.

Not to mention that to say hell is temporary implies it is governed by time. I would say that neither hell nor heaven is bound by time.

Whether or not hell is a place of torment with out end and with out relief is a question that should not discussed here.

[mitsuki lover]

I only mentioned it since when we consider wheter or not infinity is truelly infinite there are some philosophical and theological considerations that we will always end up having to grapple with.
For myself I find it hard to think of an infinity that is somehow inifiniteless,it's a rather hard concept to wrap my brain around.

[Icarus]

manglobe, I'd like to point out Technomancers post (#7), and the wonderful example of (-Inf, 0]. Working in the integers, that is the negative numbers from the end of the number line to minus one. Any mathematician will tell you that it does have an end (-1), and that it is infinite.

An even better example is (-Inf, 0) in the reals. You start out with negative infinity and include the uncountably many negative numbers. And then you tack on this one last point, zero, and you suddenly have this closed set. It has a beginning, and an end, but it's infinite.