Our universe is four-dimensional. We occupy a finite volume of an infinite Cartesian space, and because of the following mathematical fact:
we are therefore in a paradoxical situation where we are simultaneously of non-zero and zero volume.
At this point, many people would say the following (or something equivalent): a 2D being who lived on a the surface of a vast sphere, and who thought he was on a flat plane, would think he was in a 2D Cartesian space, and then say the same thing as I just have in this post. An outsider could come along and say to him, however, that there’s an extra spatial dimension in his world, which turns his infinite plane into a finite sphere, and so there’s no paradox for him.
Thus, it could be suggested that our seemingly-4D world has more dimensions - of a sort incomprehensible to us - which means we’re actually in a finite manifold.
There’s a problem.
In adding the third spatial dimension to the 2D world, we cast it into 3D, and so we now have a finite volume (the sphere) in an infinite Cartesian space, so once again, our 2D being has the paradox upon him.
I assert that in any universe comprising any number of dimensions, the zero/nonzero paradox exists. This proves the Kantian statement that the world we perceive is representation, and not the thing-in-itself. Further, a full understanding of the universe cannot be attained in such a representation, because non-dimensional conception is impossible therein.
I assume that finite/infinite=0 was not meant to be a purely arithmetic expression without any implied meaning. Perhaps you meant to include some units of space-time, so you could then conclude that the ratio of the observable universe to a theoretically infinite universe is zero. Cancelling out all the units, this zero would be a pure number, without any physical meaning.
But if you intended the ratio to be the ratio of a two-dimensional flat space to a three-dimensional volume, or perhaps a fixed-time three-dimensional slice of the universe to a four-dimensional space-time, then you might conclude that the inverse of infinite time slices is zero.
A three-dimensional timeless slice of the universe, which is a flattened “projection” that ignores or compresses the time dimension, might be considered as a state of the universe at time t.
The concept of state is useful for analytical purposes.
But it also suggests the possibility of higher dimensions of existence that are transparent to us in our world of real phenomena.
It doesn’t matter which or how many dimensions are chosen - the volume (or area, or whatever) that’s isolated will always be a finite part of the infinite (going to both ends of each dimension being considered), thence the paradox.
However, and please correct me if I am being stupid, you do not occupy an Infinity amount of space, nothing does, does it? The universe as a whole is still expanding or contracting, and if you were trying to comprehend what is beyond our whole universe, I wouldn’t recommend it. Infinity is something we can easy say to ourselves we can comprehend but I don’t think anyone understands how big infinity is.
I can see one thing though,
If you try and measure the smallest space possible, you go into infinity. But if you try and apply it to the big end, you run into a boundary… the end of the universe, with I hear ahs a nice restaurant.
There otta be a meeting to define a set number to infinity, just makes things more convenient.
I am tried of getting infantine percentiles when I want the probability that I will fill a certain volume of time or not.
I’ll focus on this particular bit. Zero, in and of itself, and infinity, in and of itself, gets tricky when applied to things like “the world”. I’m not sure here if you mean it in a purely mathematical sense, but I’ll proceed as though the goal here is some sort of truth that has some basis in reality. If you don’t mean it that way, feel free to disregard what I’m about to say.
Infinity to truly be everything, must contain “all things”. A “zero” is a thing. Therefore, infinity must contain zero, else, it doesn’t really contain “all things”–it would just contain most things. A zero is the symbol we use to denote “nothing”. If it be the case that the symbol is tethered to its meaning, then we can say that “infinity” contains “nothing”.
Likewise, nothing, by definition, is the absence of all things. It must contain the concept of infinity within its walls, or it is simply the absence of most things. If it be the case that the symbol we use is tethered to the meaning, we can say that zero contains infinity.
So in each situation, a concept that is held to be opposite each other is contained, at the very least symbolically, and at the most “actually” within the other. Hence, the paradox would here arise becuse of a faulty understanding of the opposition of “zero” vs “infinity”. They each actually have the other within themselves, and how can something be “opposite” when it contains that thing within itself?
No offence but in no way, in mathematical terms does infinity include every thing. infinity goes two ways, + and -, zero is neither. Even when dealing with space including zero in your infinity still gives you nothing…
Guy6870: Are you saying that because there are infinities at both ends of the size scales, we can’t talk about things being infinitely big, because they’d have to contain infinite infinities? If yes, I’d disagree, because that’s not what’s happening.
shinton: I do indeed want results that have a basis in reality; I never lose sight of empirical reality in metaphysics.
I’m happy to let zero be a sum of negatives, but I’m not sure about setting infinity as the set of all things - it strikes me as more of a logical word game that a meaningful statement.
a) statement that is seemingly contradictory or opposed to common sense and yet is perhaps true
b) a self-contradictory statement that at first seems true
c) an argument that apparently derives self-contradictory conclusions by valid deduction from acceptable premises
It is not a paradox to say that “we are simultaneously of non-zero and zero volume”, because the statement “we are of zero volume” is nonsense. What is it supposed to mean?
You can not divide by infinity in mathematics and equal the result to zero. Standard mathematical theory uses the concept of infinity only as a limiting value, not as a number.
It is a paradox. We know we each occupy a finite volume because we can see ourselves. We also know, from the maths, that by virtue of existing in (theoretically) infinitely long dimensions, we must also occupy zero volume. The two conflicting situations are inescapable, hence the paradox. That the second one doesn’t make sense is besides the point - in fact, if anything, it makes the paradox stronger.
You can perform division by infinity in maths. It leaves you with zero. This isn’t the issue here.
But I am still confessed, are you saying that the actual volume will live in is infantine? Because that still needs to be proven, no? Don’t get me wrong; we do live in a giant universe.
(If you have not read†the hitchhikers guide to the galaxyâ€, suggest you do, Wonderful fiction book)
I think what your meaning is time is infantine. Yes I know that time and space are the same things, maybe I can grasp how big the universe is or you can’t grasp how small it is.
Other than the definition of infantine I find this paradox amusing.
I nearly got confessed myself, but the priest wasn’t in that day
I’m talking from the point of view of the macroscopic world. The latest complex mathematical shape of the universe is arbitrary here. Nor does the fact that this paradox impinges on the major conceptual issues of the big bang and the boundary of the universe take anything away from it.
Guy, I’m aware that in mathematical terms it doesn’t. That’s why I said this:
[blockquote]I’m not sure here if you mean it in a purely mathematical sense, but I’ll proceed as though the goal here is some sort of truth that has some basis in reality. If you don’t mean it that way, feel free to disregard what I’m about to say.[/blockquote]
The issue to me is never really “what something means in a purely mathematical sense” because unless I’m engaging in some sort of mathematical mental masturbation I simply don’t care if it has no import to reality.
It reminds me of a quote by Bertrand Russell, actually: “Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.”
Very often, that seems to be the case.
Anyway, back to the thread, how would you go about defining infinity in reality if not the set of all things?
We occupy a space between the infinite and the infinitesimal. There are 12 dimensions in this realm. The Standard Model offers nothing regarding dimensions that is non-circular.
Let me ask a simple question- what is gravity’s opposing force? One must understand force and what causes it before tackling the universe and dimensions.
Fist off, I can’t place a definition to infinity, it is just that mind-boggling big! But Zero isn’t big and in my experience with including zeros in an equation (mathematical or other wise) things just don’t work out. Just last week I brought a zero to go see “snakes on a planeâ€, She ruined the entire movie! But even more serious now, now if you are saying that infinity includes everything, yes, infinity does but where will you find infinity? Not one thing comes to my mind when I think of that word. Maybe the word Universe would be a better word for you to use. My points mentioned above^^^^ are my reasoning.
Second, I am still confused about something. In school, when I learned precal, we learned how to graph trinomials (x^3+x^2+X>0). With this method we were required to plug in numbers on the number line and what ever worked, made the equation true, we shaded in that direction. Yes it is true that you can go infinitely small, but the space between 5 and 10 is still 5 even if you measured it by tenths or hundredths or googlths. I found this out when I started testing all the numbers between 5 and 6, and believe there are a lot of them.
If this isn’t the point or if I am extremely off, don’t try and teach it to me It won’t work, calc teacher found that out the hard way.
Infinity is the source of all energy, which cannot be separated from it’s source. Energy must be conserved so it cannot be added to or subtracted from. Inifinity is a manifestation of speed, not size or distance. So it is not that mind-boggling big, it is mind-boggling fast.
These are effects of infinity as true infinity is not defineable as it cannot itself be witnessed.
Infinite is infinite speed while infinitesimal is motionless. Nothing in this reality is motionless, even ‘dead’ things are dissipating. The easiest way I can put it is that we are in a certain speed.
The outer edge of infinity compresses to the infinitesimal, which expands against it. We are in the middle of this motion.
Infinity in numbers is not infinity in reality. Infinity does not mean endless.
I’m not sure I nor anyone else has witnessed “God” but there is a striking agreement on the definition of such if you bandy the word about conversationally.
In other words, I’m not sure that “witnessing” something is a criteria for “not being able to define something”. There’s a whole world of things that don’t exist that no one has ever witnessed that have definitions.
I do find your conception of infinity being motion interesting and I’ll have to mull that one over.
