beyond infinity

[Bandit]

i know this probably does not help much, but i like the two mirrors. where you look into one mirror & the reflection in the mirror gets smaller & smaller into infinity. i suppose you could start in the dark,then flip the light on & see how far you can see counting how many times you see the reflection in the mirror.
you would need two very big mirrors to start with & a telescope (LOL), then add a third mirror.

i am not very good with infinity online, but i bet we could have good discussion in person.
plus, i would have a hard time keeping God out of it.

i think the eight on its side that we were talking about is correct.
it is difficult for me to relate to it in numbers unless i literally start counting one by one.
i tend to see infinity in length or distance, without any numbers attached, not sure if that is possible.

why does it take so long to begin thinking about beyond infinity?
it does sound a lot like a new age theory...where you start & travel, then come back to your starting point.
whatever that means.

Infinity, often written ∞, is an number larger than any that can possibly be imagined. The term comes from Latin words meaning "without end."

Some people say that infinity is not really a number. It does not behave like the numbers we are used to. The numbers we are used to all have an end, but infinity has no end. And current times more and more people propose that infinety is just a abstract concept or some certain tendence of accumulating of number.

Some people say that infinity is any number, except zero, that is divided by zero.
∞ = n÷0

[_Z_]

Now imagine that situation of you the telescope and the mirrors, then visualise it as a separate entity as if only it exists! At once it is surrounded by the void or infinity, thus is infinitesimal comparatively – no matter how big something is, this always remains so!



I am sure after a couple of drinks down a quiet country pub, we would be talking sh*t until infinity ends.

I tend to see infinity in length or distance, without any numbers attached, not sure if that is possible.

It is boundless etc, numbers are metaphors, in fact all things are comparatively, thus one should perhaps be asking if; that which is not infinity is real or not? I.e. infinity is the more real. Think of this notion; ‘If you define one thing, you have to define its environment and thus another’ [add infinitum - repeat], as all things are linked there are no boundaries, thus a real object is made of atoms which are made of quantum particles, which appear from nowhere [infinity], then disappear back into it, in there life span.

It does sound a lot like a new age theory...where you start & travel, then come back to your starting point.

One cannot travel infinity; we simply arrive at the destination immediately to me it is more like an infinite door. Cycles are not relevant.

Some people say that infinity is any number, except zero, that is divided by zero.

Ridiculous If I may say so! What difference does that sum make X / 0 ? the number simply remains as it is, surely 'tis a mathematical jest. And infinity cannot be qualified in the first place, in order to arrive at a or any number.



Thanx for the quote!



They will never take me alive! [I wont give in to the scientists and atheists]



Z

[Ciel]

Why does it take so long to begin thinking about beyond infinity?


Yet clear the head of all thoughts and see already there.

Emptiness as the ground of being, without preconcieved ideology reaches to the heavens, releasing all encompassed.

[rdwillia]

Hello,

Originally Posted by _Z_

That’s just the point, nothing can be infinity, and thus infinity is nothing. Then we are defining ‘things’ against it! So firstly the definition has to change as we cannot put an edge to anything to define a thing as a ‘thing’. Zero state [statelessness] does not mean it does not exist, but then we would have to think about what existence truly is and the circle of the paradox continues. This is because we are trying to isolate infinity, whereas it should imho be seen as part of the entirety, only defined when set against a definition.

Ah, so we've been arguing the same point! So this is kind of like the "real life" point where everything equals nothing. It's so infinite that it no longer exists, or at least is no longer noticed. And to answer your question...

Originally Posted by _Z_

So I would ask can we have a nature of reality that has the quality of zero – like the void!

I would of course, have to answer yes, yes, yes!!!

Originally Posted by _Z_

Did you read the arguments I gave to the possibility of infinite planets? = not possible – I could be wrong though, I mean how do we know that anything cant happen yet only that which is relevant happens in this universe? I like to think that beyond infinity is indeed such a place and it is here right with us!

Yes, I did. I would have to concur as I have very good reason (reason enough for me) to believe you are correct in your hypothesis.

Originally Posted by Bandit

i am not very good with infinity online, but i bet we could have good discussion in person.
plus, i would have a hard time keeping God out of it.

Yes, I'm sure we could. I like Z's idea of the quiet country pub discussion. You can keep God in it as far as I'm concerned. We may not all call 'it/him/her' by that name but I believe most of us on here can relate on some level. But don't try discussing it with the other Buddhists on here as Z and I quickly found out. I think poor Z got a little frazzled, and rightly so.

Take care!

[_Z_]

Rdwillia



Ah I am with you now – it is just a case of ‘different ways to speak of the same meanings’!



Ha, yes frazzled indeed! Of course that was only because I was defending someone else’s faith i.e. Christianity, if anyone wishes to challenge my philosophy then they can just come here [to this thread - hence here it is!]. I have to say that a certain Christian annoyed me most with his post highlighting the dogmatic side of the faith! It reminds me of Christianities dark history, and why it lost its way imho. I certainly wouldn’t like to see Buddhism become similar in its intolerance and rigidity of belief, due to its worldwide expansion and popularity! I have known many Buddhists and Hindu’s, and they do tend to attack Christianity – even if via subtle mocking. I like Buddhism though as with many philosophies, it has much to show us.



A while ago I ventured into nice country pub next to a river, it had a big beer garden with small bridges gently stretching over the water, what is more; pink Floyd’s ‘dark side of the moon’ was being played and the sun was setting! What better atmosphere for philosophical debate! – Especially concerning questions like: which is better, ale or lager, or spirits, wine or beer? And who is getting them in then! By three in the morning I am sure we’ll have it all wrapped up eh – even with ‘god’ being included!

Z

[PrimaVera]

Originally Posted by _Z_

1. Infinity paradoxes. From the book infinity and the mind by Rudy Rucker.

From the book:

1.q. It is sometimes said that if infinitely many planets existed, and then every possible planet would have to exist, including one exactly like earth except with unicorns. Is this necessarily true?

I'm afraid I was "lost" at about this point, because I'm not seeing a paradox. This is, perhaps, a problem when we try to use Mathematical concepts that have very precise meanings within a broader philosophical context. The concepts associated with infinity are certainly seductive, but we must take care not to be equivocal.

In the case above, the "paradox" actually mixes two distinct meanings of "infinity" as used in Mathematics. The first concept is the number signified by a sideways "8". This is a "number" in the sense that it's used in equations (for example in the concept of a limit in Calculus).

The second concept, however, relates to sets, or rather, the cardinality of a set. When we talk about an infinite number of planets, we're really talking about a set, i.e. a collection of distinct objects that share some property that defines membership in the set.

The apparent paradox in this is the failure to realize that the cardinality of two different infinitely countable sets can be the same even though the two sets have different criteria for membership. Consider, for example, sets of numbers. The set of all whole numbers is an infinitely countable set. So is the set of all rational numbers (i.e. numbers that can be expressed as a ratio of two whole numbers). The set of all whole numbers is a subset of the set of all rational numbers, but the two sets have the same cardinality.

On the other hand, the set of all irrational numbers, that is numbers that cannot be expressed as a ratio of two hole numbers (e.g. PI), does not have the same cardinality as the set of all rational numbers. Consider a number line. Pick any two rational numbers. Between those two rational numbers, there is an infinite number of irrational numbers.

The cardinality of sets is denoted using Aleph (of the Hebrew alphabet) notation. Aleph-null is the cardinality of the set of all rational numbers. The set of all irrational numbers has a cardinality of Aleph-1.

Intuitively, it sometimes helps to think of cardinality as relating to the "density" of a set of objects. By that, I mean to say that one can, intuitively, think of the set of irrational numbers as being infinitely more dense than the set of rational numbers.

In terms of Mathematical proof, the difference between the cardianlity of two distinct sets rests on our ability to construct a logical one-to-one correspondence between elements in the two sets. If we can construct a logical one-to-one correspondence between the elements of two sets, then their cardinality is the same. If we can show that it's not possible to construct a one-to-one correspondence between the two sets, then the cardinality of the two sets is not the same.

[wil]

I personally like the fact that there are an infinite number of infinities...

[rdwillia]

Hello PrimaVera

I'm afraid I was "lost" at about this point, because I'm not seeing a paradox. This is, perhaps, a problem when we try to use Mathematical concepts that have very precise meanings within a broader philosophical context. The concepts associated with infinity are certainly seductive, but we must take care not to be equivocal.

I think that your line of thought is very clear and accurate. You obviously have a much clearer idea of how infinity works than I. But I think that your confusion stems from exactly what you mentioned; precise, mathematical concepts mixed with broader philosophical concepts.

It should clarify things, to state that mathematically, just because an infinite number of planets exist, it doesn't necessarily imply an infinite type of planet. However, I'm still confused, because if there is one thing I've gotten from this topic, it is that an infinite amount (for lack of a better word) of something... is a lot.

With my very limited knowledge of the topic at hand; If there were an infinite amount of planets, wouldn't there have to be an infinite possibility of creation or life on those planets? I'm not being facetious, I'm honestly asking because you seem like you might actually know. I have read before, in more philosophical texts, that the above "must" be true. Or is this exempt from that rule for the same reason that just because a number might be infinite it doesn't mean it's infinite outside of itself... i.e. Just because a number is infinite, doesn't mean it's also a bird.

That's where my part of the paradox fits in. I realize it's not very scientific and it's definitely not the most rational, pretty cooky and much more philosophical but... I'm saying the number is infinite within itself, very true, but then we're limiting it by saying that it can't also be a bird. I was wondering about complete infinity or the void.

However, if you accept that the two (mathematical and philosophical) infinities are separate, it makes perfect sense.

If you could help me clarify the answer to my question (above), it would be greatly appreciated. Thanks for the input!

[PrimaVera]

RDWillia,

First, while I appreciate the compliment, I must demure. People like Georg Cantor and Kurt Gödel really got this stuff. I'm barely able to wrap my head around it.

You asked:

Originally Posted by rdwillia

With my very limited knowledge of the topic at hand; If there were an infinite amount of planets, wouldn't there have to be an infinite possibility of creation or life on those planets? I'm not being facetious, I'm honestly asking because you seem like you might actually know. I have read before, in more philosophical texts, that the above "must" be true.

I'm afraid I don't know, or perhaps I understand the question. I'm not sure what you mean by "an infinite possibility of creation or life". It seems to me that you're asking whether or not an infinite number of planets implies that there must also be an infinite number of planets on which life can emerge.

If that is what you're asking, I don't quite see how to construct the line of reasoning that produces that conclusion. In order to construct a Cantor-like proof, one would have to come up with a way of enumerating the set of planets on which life can possibly emerge, and I don't know how to do that.

We can, however, say that having an infinite number of planets does not require even one planet that has any particular characteristic. This is analogous to a comparison between the set of whole numbers and the set of rational numbers. The set of whole numbers is a strict subset of rational numbers, meaning that there are elements in the set of rational numbers that are not in the set of whole numbers.

Despite the fact that one set is a strict subset of the other, the cardinality of both sets is aleph-null. In other words, the "size" of the two sets is the same. Georg Cantor proved this to be true using a proof known as the "pigeon-hole" technique.

The key factor in transfinite numbers is some form of recursive (i.e. self-referential) construction of the elements in a set. Cantor's work, for example, employed the technique of building sets out of the cardinality of other sets. Gödel took this same self-referential idea, and started building sets out of theorems, and constructed a theorem whose conclusion is that some theorems are unprovably true.

All I can really say is, when it comes to philosophy, be very careful when you make use of mathematics.

[rdwillia]

Hey PrimaVera,

Originally Posted by PrimaVera

I'm afraid I don't know, or perhaps I understand the question. I'm not sure what you mean by "an infinite possibility of creation or life". It seems to me that you're asking whether or not an infinite number of planets implies that there must also be an infinite number of planets on which life can emerge.

I think I see what your saying, and yes, that is what I was asking... kind of, not specifically but it includes that. I was asking in reference to Z's quote that you referenced in your first post.

1.q. It is sometimes said that if infinitely many planets existed, and then every possible planet would have to exist, including one exactly like earth except with unicorns. Is this necessarily true?

This was, in essense, my question. I gather from your response, that as you understand it, the above wouldn't be true. I'm missing the reasoning behind the leap taken in the above quote. I know there is some scientific theory which explains this. Somehow 'they' (whomever 'they' are) conclude that when you have an infinite number of planets, it would have to mean that every possible planet (terrain, plant life, animal life, etc.) would have to exist. But if I understand this from a purely mathematical view-point, this is not true. If the conditions don't exist (for the above) then they just wouldn't appear. Ours could still be the only planet with life. Unlikely, but possible. The only thing infinite about the planets would be there infinite amount??

Now I'm wondering where the theoretical scientists get this theory from. I can still see that it's possible, but not mathematically necessary. How about you Z? Do you remember how they explain this?

I think our posts got a little surreal for a while, but we were enjoying ourselves. And as I said before, we got into it way deeper in a spiritual/philosophical sense, often neglecting our mathematics. But I maintain my original line of thought, that I think a lot of it makes sense in that aspect as well. Take care,

~Ricky

[PrimaVera]

Ricky,

(I have a negative visceral reaction to addressing someone as "Ricky," because I hated being called "Ricky" when I was a child. But, it's your signature, so...)

Originally Posted by rdwillia

The only thing infinite about the planets would be there infinite amount??

I would say "number" rather than "amount," but that's essentialy correct.

Now I'm wondering where the theoretical scientists get this theory from. I can still see that it's possible, but not mathematically necessary.

Well, you'd have to use something other than set theory to get there, which doesn't mean you can't reach some interesting philosophical conclusions using set theory. Take a look at this.

[rdwillia]

Hello Rick,

Yes, I have internally debated dropping the "y" myself. I am fully aware of how 80's child actor-ish it is. And the popularity of Ricky Martin a few years back didn't help matters much. A lot of people have transitioned into dropping the "y" but the majority still call me Ricky. I decided to not put much concern in my name and let people call me whatever they'd like. I'm hesitant to use Richard as that has seemed to lead into other undesireable nick-names... Incidentally, I believe "Z" has signed some posts as Richard. Wonder how that works for him??? So here we are, the three R's...

Back to topic...

Your link was a great read. It covered, generally, just about everything we've discussed here. I particularly enjoyed the part about Descarte's theories being battered by relativism;

More recently, Descartes' formulation has been battered by relativism, to the point where some philosophers now question whether science itself can be objectively valued more than mysticism, intuition, or other "non-rational" belief systems.

I agree with the that we are very limited by our senses. It seems that after you get in to it so deep you'd have to come to emptiness. Set science or theorectical, after a while it gets so jumdled up that nothing make sense any more... Except of course the strict science as we currently understand it, but then that's always changing too, right? How can we possibly know anything... Aaahhh!

Thanks again Rick...

[_Z_]

Primavera, hello.

Sorry I didn’t reply sooner, virus problems on my pc.



Hmm, you don’t seam lost at all! I am seeing it from a philosophical perspective not a mathematical one, as you can probably tell, it is the resultant meanings I am after! In the end infinity is enveloped by meaning, and ‘nothing can describe it’. The maths [metaphoric measurement] only comes into the way infinity [perhaps only as a dimension] interacts with the quantum universe.

most interesting!



Rdwillia, hi.

What I would say is that ‘you cannot build up to infinity’ [I like that one], no matter how far we travel we never arrive at the end, and there is continually an infinite ‘amount’ before us, and that indeed we cannot have an infinite amount!

I would presume that if you could have an infinite amount of planets, then you could have an infinite amount of blue planets, an infinite amount of red planets X an infinite amount of blue planets with or without life etc. – but we cannot! [It would be paradoxical all over the place if we did!].

I think we are on the same wavelength, when you describe infinity as whole/complete. Thus it seams to have two distinct natures [another paradox], the ‘beyond infinity’ ‘place’, that is not definable as even infinity, then as soon as we describe it as infinity then ‘it’ tries to take on given natures of the infinite – that is to say- it interacts with ‘finite principle’, and reality is like elastic between the two [etc.]. It is like thought, first there is pure thought of nothing arising, followed by subtle thought [where thought is shaped – and hence similar to reality being shaped by principle! {Belonging to the same universal principles imo}], then fully formed thought that becomes action [in both the actualisation of the thought and synonymous in action- both of which are event manipulating].



Hope that helps chaps!



Thanx for your most interesting replies, oh and thanx for turning my head into spaghetti!



Much respect



Z

[Bandit]

Originally Posted by _Z_

Now imagine that situation of you the telescope and the mirrors, then visualise it as a separate entity as if only it exists! At once it is surrounded by the void or infinity, thus is infinitesimal comparatively – no matter how big something is, this always remains so!



I am sure after a couple of drinks down a quiet country pub, we would be talking sh*t until infinity ends.







They will never take me alive! [I wont give in to the scientists and atheists]



Z

i am not giving in to the scientists & atheists either NEVER X beyond infinity.

seriously- if we are going BEYOND infinity, then we wont be at the same place we started & we wont be there right now either. (that is new age stuff) we would be way off the track- a track with a beginning but there would be no end. like a race track where you never run out of gas!
so how is it going Z.

[_Z_]

Bandit.

I am fine mate! thanx



Ha yes, except we don’t start – we arrive there at once! But no it’s a bit like taking a leap of faith! We can skirt around the idea of ‘naked reality’ [infinity beyond infinity] only ever enveloping it – at most.

So given an infinite amount of worlds – what would yours be like?! [if you read earlier posts].



I think everyone who posts on this thread should give me a planet!



Z