i n f i n i t y

i have a problem with infinity.

its rather obvious that infinity is rather difficult for a 3-dimensional being to comperhend, but it could hold the key to existance itsself if you really think about it.

perhaps we shouldnt think about these things naturally, for instinct tells us that somhow its wrong, and we always end up confused and depressed afterwards. perhaps we shouldnt know the answer, but in the modern world, we need one even if we werent meant to to begin with. technology has increased, and therefore we are beginning to lose meaning and the will to live.

that being said,

we do not know ANYTHING for sure.
is infinity just an excuse for something that we cannot comprehend, or is it something that exists beyond our reasoning?
how can the universe never end?
but if the universe does end somewhere, wouldnt there be something beyond it? and if there is something beyond it, wouldnt it still be considered part of the universe, since the defenition of a universe is “all matter and energy” ? or is there something other than matter and energy that we do not know of or have never been exposed to?

how can we accept something that we do not understand?

infinity mut have an infinite number of dimensions, and those dinmensions must have an infinite number of dimensions of their own.

or, say if infinity was made of planes, a “plane” in geometery extends in every direction infinately, so if all matter existed within planes, wouldnt there be an infinite number of planes? and with an infinite number of planes, what would be between each one? or would that mean that it is all one since infinity cannot have anything in between?

and in this “dimensional” idea of infinity, since we only perceive in the 3rd dimension, and there are more dimensions, that would mean that there must be a parallel universe, meaning that there would be an infinite number of parallel universes? or could those universes that we do not include in our perception be intersecting or overlapping at times, meaning that part of these universes that we do not perceive would have to be part of the universe that we do see, and if there are an infinite number of other universes and our universe, wouldnt it simply be one if everything is infinite?

and what about us? would we be infinite then? making death simply an illusion, and us a part of a machine that never ever dies? and if this machine does die, since everything is infinite, wouldnt it still live on inside the universe as another form? and wouldnt we live as other forms as well?

if everything was completely infinite, then we wouldnt nw where we end and everything else begins, everything would just be a blob, but a never ending one.

but the idea of something ending is just absurd. i think of just white, blank, but how silly is it for something to just be a colour! (of course the colour would be the way we perceive it)

from how i see it, infinity would mean that every perception of everything by everyone would be completely different, and yet lead to the same thing.

when children ask about infinity, the usual answer is “think of a circle, when does it begin, and where does it end?” but that is only a line of the circle! this circle lies on an infinite plane, or floats in space if it has more than 2 dimensions (in which case it would be a shere, i suppose). but what about the interior of this circle/sphere? what about the outside? where does the outside end and where does the interior begin?!

please prove me wrong, i have only one perspective on this, but it is infinite, so perhaps i am thinking of exactly the thing you are only in a different manner.

(any form of discussion in this thread would have to be theoretical, of course)

You have to distinguish between potential infinity and actual infinity. We can comprehend potential infinity. This means we can always think of the next point in a series or a line. We cannot know actual infinity meaning literally no beginning or end. We can think of a series that runs on beyond our reasoning, but as Aristotle points out, there is always something left over from the thinking when you start considering actual infinity.

Size represents another problem because the only way we comprehend size is by using shapes that all have borders.

Now Hawking used an equation for a sphere and added an “infinity symbol” to the equation. I understand this to represent potential infinity as the shape is continually expanding.

That being said, math is an abstraction that deals with quantity and dimension only. It isolates those attributes and expands on them. If you cannot assign an actual quantity value to Hawking’s “infinity symbol” than what is the point of that symbol in a math equation?

Even if you do say the sphere is constantly expanding, as a shape, you still have to work out the finite borders to even define it as a sphere.

We can know of actual infinity in a relative sense. We can understand finite things. Actual inifinite is the opposite to finite whater actual infinity “actually” means.

Hi embracetrees:

There are some techniques that allow us to deal with infinity.

One technique is to try to deal with some infinite set such as the integers and try to compare that with another (Target) set. The method of comparison, generally used in Mathematics, is the establishment of a mapping, or function, which has the quality that it associates one and only one member of the Integers to an unique member of the Target set.

If such a function exists, then the Target set is said to be countable. Using this definition, Mathematics has proved that the Rationals are countable. And, more generally, that any solution to a polynomial equation is also countable.

The most interesting thing is that Gregor Cantor proved that the Real numbers are NOT countable.

That is to say that there are more unusual Real Numbers such as pi and e than all the other numbers put together!

It is my experience that the more you deal with techniques involving infinity, such as the one above, and the use of limits, and even more abstract concepts of compactification, the less mystifying the concept becomes.

Ed, you are talking about potential inifinity as any series of numbers can only be.

Infinity is a simple concept.

One of Spinozas prime philosophies dealed with the one ‘substance’ of which all things came, which he also called God. This is an entirely different God than represented by Christianity. The basic idea is that the Universe must have come from something, and that something came from something before that, etc… because it is impossible for something to come from nothing, and henceforth infinity is the only logical solution.

Yet, if something is infinite, infinite things come from it, and from those, and so on. Everything has come from the one true ‘substance’ it affects all things, causes all things, and technically nothing you can say is wrong becaus eof the infinite possibilities. Wrap your head around that for a moment.

Infinity IS everything, everything you can and can’t possibly imagine.

fun with zeno…

to get from point a to point b, one has to move half the distance (h) first…

before moving half the distance (h), a prior half must be moved (h/2)…

before moving half of the prior half (h/2), another prior half must be moved (h/2/2)…

before moving half of the half of the other prior half (h/2/2), still another prior half must be moved…

an infinite number of halves must be taken before movement can occur…

-Imp

See for me I can’t come close to thinking about the infinite while using numbers.
For example: 1 2 3 4… and so on right?
well then how do you go from 1.1111111111(repeating) to 1.2? You can’t count from 1 to 2. Numbers limit you to a way of thinking that is counter productive (purely in my own mind)

I prefer to think of the infinite as that which lies outside of the universe. The universe being as big as that which would be required for the existance for every possibility for matter.

It tickles my mind to think of infinity. It’s all speculation and unscientific, but it’s fun. When I say things as if I am certain about them, it is only for ‘pretends’. :laughing:

There is nothing outside the universe, therefore the universe is all-encompassing and has no boundary where it ends… or begins, for that matter. This means there is no limit to the ‘stuff’ that is the universe – matter/energy, however you want to talk about it… there is infinite stuff, and it has always existed in one form or another or a combination, and it will always exist. If absolute zero or zero entropy were even possible (I think they are merely concepts, like “altruism”) the universe would not exist. There is no reaction without action, no effect without cause, so there can be no first action, no first cause, because they imply starting from zero, which can’t be done (we distinquish between kinetic and potential energy, but in reality everything is kinetic to varying degrees, because the ‘stuff’ of the universe cannot exist unless it is in energetic motion).

“…(A) potential infinite is always finite. A potential infinite can increase forever and it will never become an actual infinite. Adding one more member to a finite set, no matter how often this is done, will simply result in a larger finite set.” --Moreland, J. P. Scaling the Secular City. Grand Rapids: Baker Book House, 1987

If a set can be added to (increased), or if there is any room left to fill, it is finite. If you can add (or subtract) one second to eternity (eternity plus or minus one second), you have made eternity a finite, measurable block of time. If you can add one inch to an infinite distance (infinity plus one inch), you have turned the infinite into the finite (translation: there never was an eternity or an infinite distance, or you wouldn’t have been able to add to them). You cannot accelerate up to infinite mph, or heat something up to infinite degrees Fahrenheit. What is the mph right before you reach infinite mph, or the degree right before infinite degrees Fahrenheit? (You can also not weigh something which is infinite – what is the ‘pound’ right before you reach ‘infinite pounds’?) Also keep in mind that our concept of “infinite” or “eternal” is rooted in our experience in this physical universe. We can not speak of an infinite set or an eternity of time which is not somehow defined by the active stuff of the physical universe. We can not refer to eternity as outside of time, when we ask if the universe has no beginning or end.

You cannot fully cross the entirety of an infinite distance, because it has no start or finish, just like zero entropy and absolute zero are merely concepts, and it is impossible to reach infinite mph or degrees. But could there be a traversable, finite section within that infinite distance (there must be), an infinite number of traversable, finite sections? You cannot describe eternity as a measurable block of time, because there is no beginning or end. But could there be a measurable block of time within eternity (there must be), an infinite number of measurable blocks of time? Just because we can’t traverse it in its totality doesn’t mean we can’t exist inside it finitely, or that it doesn’t exist.

This also has implications for our experience of time being comparable to our experience of the sun setting, but that is another thread.

heh, cool sig :laughing:

Infinity is not a number itself (and I know what merriam webster says, but he isnt a philosopher or a scientist) it is the concept of numbers going on indefinately.

Something that just occured to me as I was reading this again…

Unless I’m wrong, thought can be said to be the only real ‘thing’ in which we could foresee the infinite. IE - Every empiracle(sp? those that know me know I’m an aweful speller) experience can be chalked up to having an ending. We look at space/math but only know as far as we can see or contemplate. The weather, the waves in the ocean, they’re all complicated as hell, but they’re finite. This would explain why math seems somewhat imperfect, you can type an infinity sign and look at it, but in the end it’s just a sign.

The closest we can come to the infinite comes from within. It is the analysis of thought, the possibility that at any given point, the thoughts we have could be anything really. If the universe is infinite, and our thoughts are something that stems from experience of said universe, then in a way the closest we can come to God is not by any sort of physical phenomenon, but by thought. Perhaps this is what is meant by faith.

This actually comes as bad news. My plan was to walk to the 'fridge to get another beer but I’m not seeing as how I’ll ever make it.

not only will you never get to it, but you’ll never open it either :smiley:

-Imp

Hi jjg:

You are right.

I did a google check to find out more about potential infinity versus actual infinity.

I need to do more research, but I should note that in the article I read the author, Valentin F. Turchin, Professor Emeritus of Computer Sciences, City College City University of New York, proved that infinity was not an object like other numbers. His proof was basically the same as the proof that the set of all sets can not be a set. I have become somewhat suspicious, because the classic way to avoid this problem is to deal with hierarchies (Classes).

Then he proceeded to claim, “Fortunately, we can interpret set theory, as well as classical and intuitionist logic”. This raises a red flag for me, being classically trained, I think that the subject matter is Boolean in nature; and the Intuitionists have been discarded for some long time by virtually all main stream Mathematicians. I simply need to do more reading.

Very interesting!

Ed, this seems to be similar to incompleteness theoroms in math. Check out Kurt Goedel.

wow. internal infinity is even worse to think of that external infinity… :astonished:

can someone describe how one could come about imagining either form of infinity?

Believe it or not I was just reading about this the other day in The Philosophy of As If and the author was saying that the concept of infinity is important for the creation of certain math and theoretical problems. I bet that it’s geometry.

embracestrees… not sure if you were referring to what old gobbo was saying, but when I think of external vs. internal infinite, I just imagine a line with two arrows on each end pointing in opposite directions, with a dot in the middle of the line – you are the dot… everything to the right of the dot points outside yourself to all directions (external infinite) and gets progressively bigger on into infinity, while everything to the left of the dot points into yourself from all directions (internal infinite) and gets progressively smaller on into infinity – this is all relative to the dot, of course, and means the dot is infinitely large and infinitely small in the same instant (or in every instance, for that matter).

Hi jjg:

I love Goedel. Being old and senile, I decided not to read Goedel’s Incompleteness Theorem in the original. For which I publicly chastised myself. But I did read “Godel’s Proof” by Ernest Nagel and James R. Newman edited by Douglas R. Hofstadter just last winter. I think that his ordered numbering system of mathematical propositions is absolutely brilliant. (I never conceived of anything like that before).

I am, however, uncertain as to how his theorem relates to the matter at hand.

Is the fact that there are some true statements which can not be proved, the grounds for substituting this constructive logic? If so does that mean that the Intuitionists abandonment of proof by contradiction will stand?

The ramifications are enormous. Virtually all existence proofs will be gone along with any proof by Induction. It all seems a bit too much for me. These proofs were done by extremely brilliant people, have never been shown to be wrong, and are logically correct as viewed by classical Boolean logic.

Returning to the concept of infinity, Goedel believed that numbers were Platonic Ideals. Maybe the concept of infinity itself can be viewed in this manner. There are after all many examples of infinite sets and once we have established their essence we should be able to define infinity as that essence.

Hi Adlerian:

I don’t think that geometry is a good candidate due to the fact that it has been successfully axiomatized and even though each of the items themselves may be infinite, they are dealt with abstractly in a finite way. My guess would be the concept of limit. Without this mathematical concept we could not have developed Calculus, and Jerry would still be looking for his beer.

Ed, because of infinite recursive loops, we may not be able to prove axiomatic systems as true. This does not mean that our knowledge begins with sense knowledge and we abstract from that.

Plato had the idea that there is a world of ideals behind the material world and that our minds already have the knowledge innately to start with. This is incorrect as we learn from our sense knowledge gradually.