The Nature of Infinity

[Magical Realist]

Can infinity be a physical thing? Can there be an infinite number of
universes? Or is infinity just a concept? If it is how is it that this
concept cannot be fully conceived? Can you hold in your mind the set of
all numbers? No. At best it is just a name or a designation for an
endless sequence. Are there such things as infinite objects? How do we
know they are infinite? How about infinitesimal objects?


Some possible answers here:


What is Infinity?
http://www.mathsisfun.com/numbers/infinity.htm

 

[C C]

Can infinity be a physical thing?

If that were to mean a completed condition of material existence, of there actually being a measurement of space with micro/macro objects residing in it that is declared infinite or literally endless, then that makes it into an oxymoron of sorts, or an error of classification. A completed condition that is static in terms of further increase / expansion is still finite no matter how stunningly large it might be. If on the other hand it referred to the immeasurable, or a perpetually uncompleted circumstance -- "more" being either continually or intermittently added, or there is always the potential for more, then...

 

[Magical Realist]

If that were to mean a completed condition of material existence, of there actually being a measurement of space with micro/macro objects residing in it that is declared infinite or literally endless, then that makes it into an oxymoron of sorts, or an error of classification. A completed condition that is static in terms of further increase / expansion is still finite no matter how stunningly large it might be. If on the other hand it referred to the immeasurable, or a perpetually uncompleted circumstance -- "more" being either continually or intermittently added, or there is always the potential for more, then...

Good points. But wouldn't even an incomplete infinity be finite at some point? Namely, where it is just about to create more of itself on the threshold of non-being? I see a certain paradoxicality in the very essence of infinity that prevents us from really ever fully grasping it. It is complete, and yet it is endless. It is One, being the All, yet it transcends conception. I think there are physical infinities like black holes and singularities, mental infinities like the set of all numbers, and then the metaphysical infinity or aperion of Being itself. Being in this largest sense would be anything that "is" in any sense. In this sense language opens us to an infinite variety of modes of being--including objects and persons and properties and concepts and anything else that can be spoken of or thought about. It is through language driven thought that we encounter beings at all. Without it we would be restricted to the immediate perceptions of our own environment.

 

[universaldistress]

I'm a proponent of the idea that physical existence is not only infinite on a scale of reference we could process, as in travelling in a space ship outwards indefinitely, but is also infinite if we could zoom in indefinitely, or if we could zoom out indefinitely.

I would say how can physical existence not be infinite? Where there is something, how can there be nothing beyond that something? For me nothingness is illogical. How can there not always be something more . . ?

 

[Magical Realist]

I'm a proponent of the idea that physical existence is not only infinite on a scale of reference we could process, as in travelling in a space ship outwards indefinitely, but is also infinite if we could zoom in indefinitely, or if we could zoom out indefinitely.

I would say how can physical existence not be infinite? Where there is something, how can there be nothing beyond that something? For me nothingness is illogical. How can there not always be something more . . ?

Wow..An infinity not only boundless but bottomless as well. I like that, although it gives me abit of vertigo just thinking about it. And I think Parmenides would agree with you that since nothing can't exist, then there is only being. Tying that into infinity is a new twist, but certainly too logical to argue with. Where one being stops, another begins. And so on and so forth thruout eternity. RE: this topic, has it ever occurred to you that the vast majority of numbers could have no names? Consider all the possible word creations of language. After a certain point that would end. Language at least to my knowledge is finite. But then you'd still have all these numbers going on beyond words that nobody could ever name. I say "name" but not "designate" as a number can always be represented by other numbers. But even then it would require an infinite amount of numbers to even designate all numbers. I'm not sure there's enough space in the universe to even write these numbers out!

 

[C C]

Good points. But wouldn't even an incomplete infinity be finite at some point? Namely, where it is just about to create more of itself on the threshold of non-being?

"Potential infinity" is an open-ended procedure. There are "completed infinities" in mathematics, but that doesn't mean they correspond to or could be converted from abstract to literal concrete circumstances. By the latter I don't mean "cheating" via mere perceptions / sensations of a material environment being generated according to formula and need -- by a transcendent computer, idealist God, etc. -- for observers venturing into extreme territories of a universe whose space does not curve back upon itself. Even a dreaming, finite brain could so generate an endless world to travel through if it never died, never woke-up, and stuck to fully obeying "laws / regularities" rather than the random whims and disruptions of underlying emotional concerns. I'm instead referring to conditions as mind- or process- independent as a naive realist's version of a material world, those folks who utterly ignore any role of the brain in inferring from and converting status reports from various stimulated body tissues into the manifestations of an external, concrete reality.

I see a certain paradoxicality in the very essence of infinity that prevents us from really ever fully grasping it. It is complete, and yet it is endless.

"Materialism" can always be tossed-out the window if an infinite universe in that ontological context runs into problems (and if cosmological research claims that the universe is infinite). I just tire of people claiming they are "materialists", and then when backed into a corner by something they start mongrel-izing their metaphysics with offshoots of everything under the sun to get out of that fix. A pragmatic approach like that doesn't need to be hidden behind materialism, idealism, etc.; little point to claiming to be a member of one of those metaphysical clubs if there's not going to be strict adherence to them (materialism in this case).

I think there are physical infinities like black holes and singularities

"Physical" as in "physics" isn't being conflated with materialism above, since the former has been a mixed, chimeric monster of abstract and concrete for some time:

Scott H, Massline.org - "Physics has gotten steadily more mathematical, especially over the past 100 years. To a certain extent this has had the result of turning physicists into mathematicians, and it has also fostered the growth of mathematical idealism among physicists. Wolfgang Pauli, for example, was a fine mathematician himself, and remarked that 'The steady progress of physics requires for its theoretical formulations a mathematics that gets continuously more advanced'. And yet Pauli also thought there might be something to astrology, and other screwball metaphysical theories. Of the biggest names in physics this past century, Einstein stands almost alone in his staunch materialist tendencies. (But even if Einstein was almost alone, I am quite happy to side with him!)"

 

[universaldistress]

Wow..An infinity not only boundless but bottomless as well. I like that, although it gives me abit of vertigo just thinking about it. And I think Parmenides would agree with you that since nothing can't exist, then there is only being. Tying that into infinity is a new twist, but certainly too logical to argue with. Where one being stops, another begins. And so on and so forth thruout eternity. RE: this topic, has it ever occurred to you that the vast majority of numbers could have no names? Consider all the possible word creations of language. After a certain point that would end. Language at least to my knowledge is finite. But then you'd still have all these numbers going on beyond words that nobody could ever name. I say "name" but not "designate" as a number can always be represented by other numbers. But even then it would require an infinite amount of numbers to even designate all numbers. I'm not sure there's enough space in the universe to even write these numbers out!

It is WOW, but it's only the beginning in any exploration of absolute infinity.

It would follow that from an infinite POV all numbers have no names (except a infinitesimally finite amount around zero).

The universe is only a visibly discernible expanse. In the totality of infinity there is one atom for every number

 

[Magical Realist]

It is WOW, but it's only the beginning in any exploration of absolute infinity.

It would follow that from an infinite POV all numbers have no names (except a infinitesimally finite amount around zero).

The universe is only a visibly discernible expanse. In the totality of infinity there is one atom for every number

I could meditate on infinity all day long. There's so many rich implications. For example, some infinities are bigger than others. Like how the set of all real numbers is bigger than the set of all whole numbers. I was thinking about the infinity of all possibilities compared to the infinity of all actual beings. It seems the infinity of all possible beings would be larger than the infinity of all actual beings. Would there be a one-to-one correspondence of every possible being to every actual being? Not necessarily since not all possible beings need actually be. The number of actual beings might still be infinite yet also exclude many possibilities of being.

 

[Quantum Quack]

I could meditate on infinity all day long. There's so many rich implications. For example, some infinities are bigger than others. Like how the set of all real numbers is bigger than the set of all whole numbers. I was thinking about the infinity of all possibilities compared to the infinity of all actual beings. It seems the infinity of all possible beings would be larger than the infinity of all actual beings. Would there be a one-to-one correspondence of every possible being to every actual being? Not necessarily since not all possible beings need actually be. The number of actual beings might still be infinite yet also exclude many possibilities of being.

Contemplating the infinite is indeed mind liberating or expanding as an exercise. The ancient Greeks were great thinkers possibly due to their facination with infinite qualities/quantities as they struggled with notions of the devine [ God]

A good question I find in helping to comprehend the nature of infinity is as follows:

The question is actually very simple to answer and was answered over 8000 years ago... [ apparently ]

• If the universe is infiinite in size where would you find it's center?

The same question, but with more difficult ramifications, can be applied to time.

• If time is eternal where would be the center between past and future?

 

[Magical Realist]

Contemplating the infinite is indeed mind liberating or expanding as an exercise. The ancient Greeks were great thinkers possibly due to their facination with infinite qualities/quantities as they struggled with notions of the devine [ God]

A good question I find in helping to comprehend the nature of infinity is as follows:

The question is actually very simple to answer and was answered over 8000 years ago... [ apparently ]

• If the universe is infiinite in size where would you find it's center?

The same question, but with more difficult ramifications, can be applied to time.

• If time is eternal where would be the center between past and future?

Anywhere and anytime?

 

[Quantum Quack]

Anywhere and anytime?

yep..spot on as far as I know it to be...

but it is where this question leads to that has greater relevance, as it asks you to decide as a matter of choice where the center of an infinitely large universe would be.

It is your ability to choose freely [freewill] that is exemplified by the question and answer.

If we assume that the universe is indeed infinite in size and there is no boundary as such then any where you choose the center to be is valid as it is with any one else who chooses to do like wise. As all persons choices are equally valid all persons have freedom to choose "infinitely".

Therefore the "imagination" has the freedom to go to the center, where and when the person chooses it to be.

Examples:
I can imagine myself living in the year 1040 as William The great forced his new system of Justice on the Brits.
or I can imagine myself to be living in a universe 2 billion years ago in a galaxy far, far away... etc etc.. if you get my point.
The center of my universe is where I am thinking about going to.....so I create a center and go there...sort of thingo...
You therefore can be what ever you choose to be...

 

[hansda]

I think Infinity is ONE.

Just because of our limitation of perception, we can not see this as one and instead see this as infinity.

 

[universaldistress]

I could meditate on infinity all day long. There's so many rich implications. For example, some infinities are bigger than others. Like how the set of all real numbers is bigger than the set of all whole numbers. I was thinking about the infinity of all possibilities compared to the infinity of all actual beings. It seems the infinity of all possible beings would be larger than the infinity of all actual beings. Would there be a one-to-one correspondence of every possible being to every actual being? Not necessarily since not all possible beings need actually be. The number of actual beings might still be infinite yet also exclude many possibilities of being.

It depends on the definition of your possibilities. If the possibility means a being that could exist in infinite existence through a process of evolutionary increments on matter, chances are it is out there, but only if it is possible in this way. It doesn't have to be out there now, only have been, or will be, OR is.

I would say Infinity has no centre. There is only POV. An infinite amount is immeasurable, so there is no way it can be divided into two equal parts and a middle ascertained. One can only choose a coordinate position, or view it from everywhere at the same (at all) time/s (conceptually). But even when viewing from a POV one must conceptually never slip into the erroneous interpretation of infinity referred to from a fixed-type semantical position (position that assumes an "individual's type view" that influences language used back to explaining infinity from a POV). Hope that is understandable.

So: "If the universe is infinite in size where would you find it's center?" is an impossible question as using my axiological stance/definitions the question contradicts itself.


And: "If time is eternal where would be the center between past and future?" By saying past and future one is taking a POV type position when constructing the question, as there is only the present when the question is asked. One could say that the present is the middle between past and future from a POV stance (a specific and limiting axiological stance) but infinity doesn't recognise your position or existence in its construction. It just is infinite and eternal. Saying "middle" when regarding eternity or infinity is for me an erroneous assumption/conceptualisation because something that has no end is not measurable, and can't be split into equal parts. To assume to be in the centre smacks of Aristotelian physics assuming the earth is the centre of the universe (false and assumptive axiological structure).

?

 

[universaldistress]

I think Infinity is ONE.

Just because of our limitation of perception, we can not see this as one and instead see this as infinity.

This makes sense because if infinity is truly infinite, then there can be only one physical infinity because this infinity would include any other measure or infinity within it. Infinity being infinite AND "All".

 

[Quantum Quack]

This makes sense because if infinity is truly infinite, then there can be only one physical infinity because this infinity would include any other measure or infinity within it. Infinity being infinite AND "All".

yes, I agree .. you cannot have an infinity that is not absolute... no such thing as a partial infinitey...

 

[Quantum Quack]

I would say Infinity has no centre. There is only POV. An infinite amount is immeasurable, so there is no way it can be divided into two equal parts and a middle ascertained. One can only choose a coordinate position, or view it from everywhere at the same (at all) time/s (conceptually). But even when viewing from a POV one must conceptually never slip into the erroneous interpretation of infinity referred to from a fixed-type semantical position (position that assumes an "individual's type view" that influences language used back to explaining infinity from a POV). Hope that is understandable.

So: "If the universe is infinite in size where would you find it's center?" is an impossible question as using my axiological stance/definitions the question contradicts itself.

interesting point, thanks...

Given that we have an immessurable infinite amount to deal with.... it is easy to say that any point in that infinite amount could be considered as it's center.
Due to the fact that if one measures the distances in any direction from that chosen point those distances must be infinite.

Assume an infinite 2 dimensional plane [ could just as easily be 3 dmensional ]

The key to the question I feel is in asking YOU.. where you would find the center of an infinitely large universe.
It is you that exists in this infinite universe, therefore an existential form of geocentrism POV could be considered as valid.
And the question does imply a existentially fixed position within an infinite universe...
and relies on the defintion of the word "center". [being a point in a volume of space that has equal volume distances surrounding it..]

 

[universaldistress]

interesting point, thanks...

Given that we have an immeasurable infinite amount to deal with.... it is easy to say that any point in that infinite amount could be considered as it's center.

Easy to say but impossible to rationalise.

Due to the fact that if one measures the distances in any direction from that chosen point those distances must be infinite.

An infinite distance cannot be measured. Infinity is not a quantifiable concept.

Assume an infinite 2 dimensional plane [ could just as easily be 3 dmensional ]

A point can be chosen but it is not central. There is no centre. This diagram is a small POV vista.

The key to the question I feel is in asking YOU.. where you would find the center of an infinitely large universe.

There is no centre, only one's position/POV

It is you that exists in this infinite universe, therefore an existential form of geocentrism POV could be considered as valid.

One may wish to hold erroneous concepts (erroneous within situation where existence IS infinite) in trying to rationalise this context/axiological structure but the nature of infinity is in contradiction with any assumption of nucleation.

And the question does imply a existentially fixed position within an infinite universe...

In assuming the axiological structure (that the finding of a middle to infinity is possible) one is implying distances out from the middle are measurable and therefore finite (infinite distances are immeasurable). This focuses the context to a finite volume, therefore assuming the stance I state.

and relies on the defintion of the word "center". [being a point in a volume of space that has equal volume distances surrounding it..]

There are no measurable 1,distances, or 2,volume distances because an infinite distance of any type is immeasurable, and therefore unquantifiable and by nature un-applicable within context of existence being infinite.

One can't say "Given that we have an immeasurable infinite amount to deal with" and then go on to assume measurable distances are involved.

 

[Quantum Quack]

Easy to say but impossible to rationalise.
An infinite distance cannot be measured. Infinity is not a quantifiable concept.

A point can be chosen but it is not central. There is no centre. This diagram is a small POV vista.

There is no centre, only one's position/POV
One may wish to hold erroneous concepts (erroneous within situation where existence IS infinite) in trying to rationalise this context/axiological structure but the nature of infinity is in contradiction with any assumption of nucleation.
In assuming the axiological structure (that the finding of a middle to infinity is possible) one is implying distances out from the middle are measurable and therefore finite (infinite distances are immeasurable). This focuses the context to a finite volume, therefore assuming the stance I state.
There are no measurable 1,distances, or 2,volume distances because an infinite distance of any type is immeasurable, and therefore unquantifiable and by nature un-applicable within context of existence being infinite.

One can't say "Given that we have an immeasurable infinite amount to deal with" and then go on to assume measurable distances are involved.

Please understand that I accept your arguement based on the semantic "rules" understanding you are working with.

I can only say the following and leave it to you and others to work out...
"I am standing on a hill top and I look to my left and look to my right and look forward, behind up and down, and realise I am in the center of an infinite universe. For every where I look immeasurable infinite distance exists."
If you can state: that in any direction a finite distance exists then I can not state I am at it's center. If I can state that immeasurable infinite distance exists in any direction from where I am then I can claim to be at it's center.
I guess the point is that even though infinite distance is immeasurable one can easilly say that all infinite distances are equally infinite. Therefore all distances away from my POV are equal. In saying this a center has been established.
(d= infinity) = (d = infinity)
(d= infinity) - (d= infinity) = 0
equivilance established....

 

[universaldistress]

Please understand that I accept your arguement based on the semantic "rules" understanding you are working with.

I can only say the following and leave it to you and others to work out...
"I am standing on a hill top and I look to my left and look to my right and look forward, behind up and down, and realise I am in the center of an infinite universe. For every where I look immeasurable infinite distance exists."
If you can state: that in any direction a finite distance exists then I can not state I am at it's center. If I can state that immeasurable infinite distance exists in any direction from where I am then I can claim to be at it's center.
I guess the point is that even though infinite distance is immeasurable one can easilly say that all infinite distances are equally infinite. Therefore all distances away from my POV are equal. In saying this a center has been established.
(d= infinity) = (d = infinity)
(d= infinity) - (d= infinity) = 0
equivilance established....

Same logical issues. You are just reiterating false assumptions You assume a centre of infinity is a rational concept. You are assuming infinity is measurable ("equally infinite": things can't be equally infinite as infinity can't be measured. Saying equally you are installing a method of quantification that conceptually attempts to fix down something that cannot, by its nature, be fixed down or quantified. They are not equal, just infinite; two directions from a fixed point (POV) that can't be used to understand something that is infinite).

I just say that your axiological stance is contradicting the idea that existence is infinite, in fact it contradicts itself. Your explanation doesn't settle the physical issues involved. I think my logic is sound.

We can beg to differ, agree to disagree. That is all.

 

[Quantum Quack]

Same logical issues. You are just reiterating false assumptions You assume a centre of infinity is a rational concept. You are assuming infinity is measurable ("equally infinite": things can't be equally infinite as infinity can't be measured. Saying equally you are installing a method of quantification that conceptually attempts to fix down something that cannot, by its nature, be fixed down or quantified. They are not equal, just infinite; two directions from a fixed point (POV) that can't be used to understand something that is infinite).

I just say that your axiological stance is contradicting the idea that existence is infinite, in fact it contradicts itself. Your explanation doesn't settle the physical issues involved. I think my logic is sound.

We can beg to differ, agree to disagree. That is all.

If I state that the notion of infinity is in itself an irrational notion [incomprehensable] then it would follow would it not that all notions that extend from it are equally irrational?
Is infinity a rational notion?
there's an old bit of wisdom something to the effect of
"Agreement is not necessary but understanding each other would be nice"