Thu, Apr 26, 2007 Permanent linkCan there be novelty in an infinite world? Wouldn't everything we think is novel have the opportunity to occur again? And again and again ad infinitum until every possibility occurs somewhere?
Are you saying that the universe is finite but that there are infinite possibilities of occurance in it? In which case wouldn't an infinite universe have had the opportunity to occur as well?
...hmm...now I don't know if I'm being too abstract for my own good. I find the idea of infinity troubling and almost impossible to deal with without getting into a pattern of maddening circular logic. But I have the sneaking suspicion that believing in infinity is no different from believing in a god - in that it seems like an easy way out of explaining the universe.
I don't know...obviously there's more thinking to be done - until it all gets too heavy and rolls back down the hill...an ironic metaphor since Sisyphus rolled his boulder for eternity himself.
Thu, Apr 26, 2007 Permanent linkWait a minute...I said:
Are you saying that the universe is finite but that there are infinite possibilities of occurance in it?
Scratch that...that doesn't work for me either - a universe with a finite amount of matter would have to have a finite (albeit huge) amount of possible incarnations of that matter.
Thu, Apr 26, 2007 Permanent linkI like the idea that everything already exists in the cosmos anonymously until the concept, object or form is discovered/born, named and thereby assigned an identity. I guess this would be the "formality of occurring."
Fri, Apr 27, 2007 Permanent linkAl, yes, I think I said the opposite of that; an infinite universe with a finite amount of physical material (condensed out of hyperspace?). I like the Wizard's idea as well—everything existing as a potential.
I think the universe is finite only in the concept you have of it in your own mind. As you think about it, you regard it as a whole; a concept; an idea. however, because it seems to be part of a potentially infinitely ongoing process that is ever evolving over time, it does not necessarily end, and in that way it is infinite.
Fri, Apr 27, 2007 Permanent linkHmm, I like that Superfamous - even if it were to end, we (you, me, cupcakewizard, grains of sand and everything else) would end with it. That's interesting. I think I have a hard time wrapping my mind around an infinite universe having a finite amount of material in it. But I guess it's to be expected that such things would be difficult to conceptualize. But I definitely see your point of the universe as an ongoing process.
cupcakewizard, your idea reminds me of the quote from Michelangelo:
In every block of marble I see a statue as plain as though it stood before me, shaped and perfect in attitude and action. I have only to hew away the rough walls that imprison the lovely apparition to reveal it to the other eyes as mine see it.
Neat.
Sat, Jul 14, 2007 Permanent linkon the first day of an astronomy class i took a while ago, the professor was trying to explain that the outter space was infinite, and just as he was saying, "it's very hard for many people to wrap their head around this" a girl raised her hand and asked, "but where does it end?"
i just realized that i only just realized what that means. the dictionary says the universe is believed to be 10 billion light years in diameter and expanding outwards. but what is it expanding into? where did that space come from? can we safely say that this space is devoid of matter and therefore infinite? is the one we know the only big bang that ever happened?
holy crap, it's so easy to blow the human mind.
Tue, Jul 17, 2007 Permanent linkIt almost seems pointless to think about it too much (although I admit the value of thining about it from time to time). It's like looking at a page of completely foreign language and trying to guess what it says: "well this kinda looks like a g...and this looks like a bird..."
Tue, Jul 17, 2007 Permanent linkthough i agree to a point, that analogy actually supports the value of thinking about these things...because that's precisely the method by which we came to understand hyroglyphics or cuniform, for example, and if any alien intelligence ever sends a message to Earth, like in Contact, we'll have to do the same thing. i'm personally not a huge fan of the blatent why are we here? line of questioning but, speaking of languages, its rediculous how just the slightest re-framing of an issue that's been turned over for milennia can bring unarticulated, or unimagined concepts into focus, even if no conclusion to those unanswerable questions is ever reached. and infinity will keep us from ever figuring out the ansers to those questions perhaps. In that case infinity itself is kind of a funny/pointless/maddening thing to think too much about. case closed.
Wed, Dec 19, 2007 Permanent linki haven't read all the comments, so this point may already have been made.
but. how do you know that houses aren't grains of sand that are houses?
or that the emotion of sadness is in fact grains of sand that are sadness?
definitions are boundaries, are if you make something infinite you remove its boundaries, and thus its definitions.
infinity is boundless, and thus it is anything and everything. it has to exist, simply because it includes everything that is leveled against it.
Wed, Dec 19, 2007 Permanent linkInfinity! What a term! But do we have the language to explicitly and inherently define what do we mean by infinity? For any description to have any meaning we need a contour, a limit if you like, a border that defines, the finiteness of the term. So in fact the term infinity be it of grain of sands, of quarks,of energy, or of mind for that matter, needs a measure.
The yardstick of math, of physics, or of poetry?
These are all different methods, manners, fashions, in fact descriptions (some total conceptual languages) that allow us to cross map into/unto another mind system. so basically the question I remain with is: what is the best measure to define infinity so as cross mapping will make sense in a philosophical context?
Some have claimed that our minds are not meant to deal with the immensity of infinity and hence we need not bother ourselves with questions of infinity since the game is lost a priori.
Of course if that was the case we wouldn’t be able to have this very conversation, a cross mapping in itself.
Wed, Dec 19, 2007 Permanent linkWhen I was young, I remember thinking about the idea that the universe was infinite and saying, hmm...
If there is an infinite amount of time that passes, and the universe is never in the same state at two instances, doesn't that mean that every possible state of the universe will exist and be real at some point? Including completely absurd ones? Does this mean that I will experience every possible experience, die in every possible way and somehow become alive again, simply because every state must happen?
It took me a few years to realize why this argument is wrong... but it was still a nice thought, and I enjoyed it for a few years there.
Wed, Dec 19, 2007 Permanent linkjust because something never ends, does not mean that it contains absolutely everything. infinity certainly exists, at least in theory. think about the countable numbers: start with one, and take its successor. do this ad infinitum and you've got the infinitude of natural numbers. this is an infinite amount of numbers, but it does not, for example, contain all of the rational numbers. hence, a set of things can be infinite without including everything. it seems that the working definition of infinity here is wrong—infinity implies that a set of some stuff is never-ending, not that it is all inclusive. the notion of "everything-possible" that has been discussed here is something entirely different, and probably does not exist—but infinity certainly exists if only in its mathematical definition.
Thu, Dec 20, 2007 Permanent linkPointing to fractals as evidence of the infinite to me is like pointing to the existence of the word "infinty" as proof - I suspect they are both human concepts.
To my understanding, there are no true fractals in nature. However self-similar a fern's leaves and branches are there's a point at which the similarity breaks down. This is even true with our simulations of fractals: if we get close enough to the computer screen, we'll see individual pixels which no longer represent the overall pattern. Fractals are ideas, and the image or animated simulation of one is a representation of that idea rather than an example of it.
We look at the patterns we find in nature (fern leaves, the orbit of planets vs the orbitals of atoms), and being playful creatures, extrapolate them "further than we can possibly imagine!" (i.e. infintiy) and "faster than a speeding locomotive!" in the same way we see rabbits in the clouds. Much like these rabbits, a fractal is a story. A story that says, "isn't the world fascinating!"
I am inclined to agree with john and Wildcat's thoughts on the limitations of our words in defining such things. And I must say, folkert's vision of a universe with infinite possibility, but finite or novel substance, strikes me as wonderfully weird (as Joakim would say). I can't help but think that the universe is not made of "natural" or rational numbers or mathematics - which like fractals - are practical concepts we've come up with in trying to function in a universe we can't yet wrap our minds around. Math is the story of our understanding of the universe. We've done fantastic things with it, yes. We've soared above mountains. But a bird does the same thing and has no use for math.
The universe doesn't contain "a set of some stuff" gap23, but a set of all stuff that doesn't care about mathematics. I'm convinced the universe is simply one, weird thing.
Thu, Dec 20, 2007 Permanent linkI'm sorry, I'm a mathematician.
I have to believe it, it's part of my job.
Mon, Dec 24, 2007 Permanent linktrubers, that strikes me as a bit of a cop out.
You can believe in the mathematical concept of infinity without necessarily believing that any real, tangible thing is "infinite".
A large part of this seems to be semantics to me. All the mathematicians are going to look at this, and say of course there are things that aren't finite, its very easy to find examples of infinite sets.
But that's not really what al is talking about. Fundamentally, finite things are "bounded" and infinite things are "unbounded", even in mathematics. For something to be truly unbounded, how can it even have a definition, since defining something does constrain it? (as John pointed out already)
The Mandelbrot fractal may have an apparently infinite level of detail, but its existence is certainly "bounded" by the rigid, algorithmic definition of it in terms of series of complex numbers which converge or diverge. So is it really, truly and completely, infinite?
In a sense, I think that everything that is real is constrained by its existence and so fails to be completely infinite.
Mon, Dec 24, 2007 Permanent linkYou can't prove infinity. It is a theory, very much like complex numbers in mathematics.
Saying you don't believe in infinity is the same as saying you don't believe in the 2nd dimension, something mentally tangible, but not physically possible in the 3rd dimension.
Tue, Aug 19, 2008 Permanent linkJust for the record:
Many humans have tried to explain to us that we cannot understand concepts that are beyond us, concepts such as infinity (because we are finite systems), or for that matter unconditional love (because we are conditioned).
I beg to disagree; we are an intelligence that can self-metamorphose by its own and on its own. We are a kind of mind that can not only create the tech singularity because we will it, we can do much more than that, we can bring about our own transformation via our own mind singularity which can and maybe/probably will give us the capacity to break through the conceptual barrier we are now facing.
from Wildcat's Transbeing
Tue, Aug 19, 2008 Permanent linkinfinity is just a relative concept.. it's more like an adjective rather than a complex philosophical theory. it exists as a word explaining an unimaginable countless boundary. i read some of the comments and each explained a different usage of the word in different sciences, like mathematics, physics, psychology, and ...
perhaps the most satisfying definition of infinity is in optics: "an object which is much further away than the focal length of a lens is said to be "at infinity", as the distance of the image from the lens varies very little as the distance increases further."
Tue, Aug 19, 2008 Permanent linkI think that folkert's initial response was as close to the mark as one could get. Our imagination itself is a perfect example of this description of infinity. Humans are probably the only species capable of drawing from this resource of infinite potentials (imagining concepts which have not yet formally occurred/objects which do not yet exist) and bringing them into existence. To reject infinity is to embrace the opposite, in which case we are stuck with what we have, with no possibility of true 'creation'. Albeit, it may be rare that these potentialities become reality—more often than not, reality simply gets recycled—the very notion of them proves their existence, in turn opening the floodgates to the infinite beyond.
Tue, Feb 23, 2010 Permanent linkI'd like to pick up at meganmay's first post:
I love to think about stuff like this in a strictly amateur way. Here is my bit:
One reason it might be hard to accept infinity (per the argument above), is that we as humans have no direct way of experiencing it. (At least not in this phase of living, if we take into account the possibilities outlined by various religious outfits.)
Viewed from a different perspective, we are equally unable to experience "finiteness", if understood as a meta concept. The beach ends somwhere, just as each grain of sand does ... but I still have to experience something to end without something else beginning or continuing.
I like this puzzle and I have to admit that the various theories, scientific or religious have yet failed to convince me of either. Which makes worthwhile discussing the topic with people who have their own opinion about it ...
Tue, Feb 23, 2010 Permanent linkThere are many different kinds of infinities - different aspects of things that we can grasp cheaply through the generative art or expensively, by writing smart ideas.
Here's an example of an invention that was used for the analysis of the dynamical systems before the computers. It features a strange map of all natural numbers that seems to crisscross and bisect the infinity...
http://en.wikipedia.org/wiki/Sharkovskii%27s_theorem
Tue, Feb 23, 2010 Permanent linkTommi, thanks for digging this post
that's a very funny discussion!
It's ironic how humankind can digress endlessly about the topic of infinity / eternity ;)
Wed, Feb 24, 2010 Permanent link* I am certain that we possess the sense of infinity. We can feel the implications of an object such as fractal and project the procedure of its creation into infinity. Suddenly we can know something about that "infinity", even though it is a simulation.
* Infinity is in the structure of matter for example, in every curve there is the number pi. It is present as a natural constant. The physical, dynamical processes function by already using pi in its infinite form, or they are approaching to the pi. The infinite randomness in the system could overload and hide the accurate reading of the pi in the system. Without the infinite randomness the physical world would be uninteresting.
* Very large numbers of anything are equivalent to infinity in practice.
Thu, Feb 25, 2010 Permanent linkThe mind always seems to conjure concepts to give a working scope/realm to a problematic instance of unknown proportion.
For instance in chemistry the avogadro constant for a defined pressure dynamic, the constant has an infinitude of responsive applications based on the environment of it's conceptive notion.
Whether a belief is held true or not seems best suited to the applicable scope of intent in human pathology. Mammalian brains tend to be fragile in the balance of emotionally ratifying security in an insecure world. We are lead to believe that representative bodies are infallible when in actuality they can be far from what is expected.
Atleast we can believe in our security of disbelief for some time and even time is but a representative scope of relative spatial inference.
Is a utilitarian prerequisite imperative for belief and would the lack thereof give no meaning?
Fri, Jun 18, 2010 Permanent linkWhat a great post and interesting comments.
Tommi said:
One reason it might be hard to accept infinity (per the argument above), is that we as humans have no direct way of experiencing it.
I completely, but respectfully, disagree. How about the spiritual/psychedelic experience? I think that there are some people here that might be able to relate... I've felt infinite. I've been the Universe and everything in it. I was the Wholeness, nothing more, nothing less.
These kinds of experiences are usually ineffable to describe with our language. In my opinion, the only way to understand Infinity is to actually experience it.
Love the illustration! Much enjoyed your grain of sand examples, with which, I think, you've given me the arguments I need to state the opposite point, namely that everything is infinite.
Everything is potentially everything until it undergoes the formality of occurring. From that moment on, every other potential form or state that the grain of sand could have possibly had is cancelled out.
In the same way that physical matter is pretty much entirely made up of empty space with only a few instances of actual substance (the nucleus of an atom is comparable in scale to a fly in the middle of a sports stadium), I think that most of the cosmos is made up of infinity, with a few desolate islands of "novelty"—things that have undergone the formality of occurring.
So, I think that we (you, me, the world, the turtle with fifty-three heads) are finite moments of extreme novelty and complexity in an otherwise infinite sea of potentiality—things that have undergone the formality of actually occurring.
A finite entity, as opposed to infinity experiences boundaries and limitations (death, not being able to fly, trees, the body, mutation, etc.), I think that life is simply a set of constraints which is where you can see it contrasting with infinity. Potentially "everything" versus "something".
We are moments of extreme novelty in vast contrast to the infinite nature of reality.
Maybe.