The Infinity Experience: Can we truly comprehend infinity?

[plus]

Originally posted by drag
Greetings !

I believe a mathematician would disagree
with some of that, but I'm not one so I'll
just keep my mouth shut.

Correct.

There is a huge amount of research done into the field of infinity, and I have studied some of it. You may want to find out about the extended real line and some really rigorous work there.

If we are to talk rigorously about infinity, then we should all have Phds in maths. We cannot hope to get to grips with some of the facets of it in this thread, which is written mostly by laypeople.

Rigorous mathematics and physics cannot be handled by conceptions alone. It needs to be accompanied by technical detail.

 

[RuroumiKenshin]

Could you apply Zeno's paradox to understanding infinity?

 

[drag]

Originally posted by Mentat
Alright, let me explain: I am not talking
about mathematical infinities. I know that
there can be more than one infinity, in maths,
and that there can be "bigger" infinities.
However, I'm talking about space itself.
If you take a space that is infinite (as in,
having no end), how could you possibly add
more space to this? Even if you could,
(though I don't think you could) your result
would be the same as before (infinity), and
thus you haven't made it any bigger at all.

Like I said before that message - things inside
will get farther or closer apart. You'll have
the symptoms of growth.

What you seem to be bothered by are the borders,
but infinity has none, does it ?

Live long and prosper.

 

[damgo]

You don't need a math PhD to play with infinities rigorously... basic courses in set theory and analysis should do. You can perform arithmetic on infinities in several senses -- cardinal and ordinal arithmetic, by using systems such as the hyperreals or surreals, and prob some others I don't know about. But back to the original question...

When we talk about the expansion of an infinite universe, we don't mean its "total size" gets bigger in the way, say, a balloon gets bigger as we blow it up. We mean that the distances between objects in the infinite universe gets larger. So if there are originall objects at {..,-2,-1,0,1,2,...} they will move to {...,-4,-2,0,2,4,..} after some time, and continue to get further apart.

 

[wimms]

Originally posted by drag
First of all, it's physics not mathematics.
Second, all the physical laws currently
recognized are limmited by the BB and no
one, so far, attempted to expand them to that
point and beyond because we simply have no idea
about it, again - so far.

Ah, now I'm lost. Why did you find important to object that so strongly?

I believe a mathematician would disagree
with some of that, but I'm not one so I'll
just keep my mouth shut.

If the Universe's dimensions were rings
for example - where are the limmits ?
Higher dimensions ?

ok, let's leave infinities to Phds in math. They feel touched when laymen talk about their pets. Although extended real line specifically warns that infinity is not a number and should never be treated as number, but only as function.

In regards to rings, what you mean by ring? 2D object? 2D planes are infinite, ring is only subset.

How about - not anything. Makes a difference ?

What is your definition of logic ?
Is logic (in your definition )the absolute
guide of the Universe ? Or maybe, your logic
can still outsmart you (like relativity outsmarted
physicts before - and without logical discrepancies) ?

More to the point - the Universe is not logical.

not anything vs nothing - no difference. There is no reason to exchange definitions of logic, that will go too far off topic. There is probably also huge research in that area constantly heating up. Suffice it to say that logic is the basis of any and all proofs you'd ever heard of. My application of logic may be flawed, in which case you may show my error. I reached such thought as I showed, and unless you can show my error, I see no reason to be sarcastic.

Universe not logical? kidding right? Some argue that universe is not only logical, but rather IS the thing itself.

 

[Royce]

As mentioned in the beginning of this thread "Infinity is not a Number"; nor, is it a Limit. Infinity can expand infinitly as Infinity implies no limit, no edge, no boundry, no end. To use a math analogy the number set is infinite and can be expanded infinitly because I can always add a 1 to any infinite number that you can name.

 

[Stormy]

Technically you can't add 1 to infinity because you are already there,
for instance, if you say "infinity" and then I say "infinity + 1" then that doesn't count because infinity + 1 was already stated in the term "infinity."

Think about it and it will make sense

 

[Mentat]

Originally posted by damgo
You don't need a math PhD to play with infinities rigorously... basic courses in set theory and analysis should do. You can perform arithmetic on infinities in several senses -- cardinal and ordinal arithmetic, by using systems such as the hyperreals or surreals, and prob some others I don't know about. But back to the original question...

When we talk about the expansion of an infinite universe, we don't mean its "total size" gets bigger in the way, say, a balloon gets bigger as we blow it up. We mean that the distances between objects in the infinite universe gets larger. So if there are originall objects at {..,-2,-1,0,1,2,...} they will move to {...,-4,-2,0,2,4,..} after some time, and continue to get further apart.

This is what drag, and others, keep saying, but I disagree. If someone speaks of the spatial dimensions themselves as expanding, then it doesn't follow that just some things could be getting farther apart, but all things should be getting farther apart. And if all things are getting farther apart, then this has to be happening throughout the entirety of space. Of course, there is not "entirety of space" in an infinite universe, which is why I don't think that everything can get farther away from everything else, in an infinite universe. Thus, the spatial dimensions cannot expand, in an infinite universe, IMCO (in my current opinion).

 

[Mentat]

Originally posted by wimms
not anything vs nothing - no difference. There is no reason to exchange definitions of logic, that will go too far off topic.

You were the one who asked what "nothing" was. He is giving you a perfect answer - it's not anything. There is no "it" to speak of. "Nothing" doesn't refer to anything, and can only be used in exagerations; such as "There's nothing to eat in here", when in fact there are insects crawling around (just an example). If you use the term "nothing" to signify something, you will get a nasty semantic debate - the likes of which I've tried to prevent, with my "Exercise in "Nothing" Semantics thread.

 

[wimms]

Please, read before you argue. I've never implied one should think of nothing in any other way.

 

[Mentat]

Originally posted by wimms
Please, read before you argue. I've never implied one should think of nothing in any other way.

Oh really?

Originally posted by wimms
By definition, beyond these boundaries there
must be Nothing. Now ponder for a moment,
what is Nothing?

 

[Royce]

Stormy,
I disagree. Infinity means no limit, no boundry. To say that I can not add a one to infinity is saying that infinity is a limit which is an oxymoron. I can add infinity to infinity and still have infinity mathematically. Physically infinity "simply" means no edge or boundry. There is no limit in infinity to stop our universe from expanding even if it is infinite. There is more and more evidence however that our universe is closed, a sphere if you will and is expanding faster than the speed of light into an infinite void. The thinking is more and more that we live, and our entire universe is, inside a black hole that is expanding from the singularity that it was "before" the Big Bang. Indeed in another reference system it may still be a singularity. What is the void or what is beyound is anybody's guess. Nothing is mine. No time. No dimension. No spacetime. Nul space is what I call it. it is not even space as we think of it much spacetime. It is literly a void, as hard as that is to conceive of. In comparision it make infinity a piece of cake.
Cake unfortunatly is finite and I better go get some before it disappears into the black hole that is my grandson.

 

[damgo]

>>Of course, there is not "entirety of space" in an infinite universe, which is why I don't think that everything can get farther away from everything else, in an infinite universe

Sure there is, it's just infinite. What's the problem? How are the points {m | m is an integer} with location (m*t) not all getting further apart as t increases?

 

[Stormy]

Originally posted by Royce
Stormy,
I disagree. Infinity means no limit, no boundry. To say that I can not add a one to infinity is saying that infinity is a limit which is an oxymoron.

But that is my point infinity has no limit so if you say infinity then you also mean infinity + X because infinity is, of course, infinite. It has no limit so encompasses all.

 

[Locutus]

Originally posted by Stormy
But that is my point infinity has no limit so if you say infinity then you also mean infinity + X because infinity is, of course, infinite. It has no limit so encompasses all.

This is not true. Let us imagine the set of real numbers between 0 and 1. There are an infinite number of numbers between 0 and 1, but that does not mean that any number must be part of this infinite set. 2, for example, is not encompassed by this infinity.

Infinity is quite simply any quantity that exceeds our means of measuring it. In the case of mathematics, infinity is any number that cannot ever be reached or represented by our numbers.

I find the case of an infinitesimal number easier to use to explain the above statement. An infinitesimal number is infinitely close to 0. It is not 0, but we cannot measure its separation from 0 using any conventional mathematics.

Thus we have established that infinity is not part of the standard mathematic universe of complex numbers. When one says "infinity + X" they are adding to completely dissimilar terms; it is analagous to one saying "22 grams + 18 miles".

 

[Stormy]

Ah, but that is the difference between the mathematical and physical point of view. In maths you have to have a starting point and an end point, e.g. 0 and 1 but even though there is an infinite number of values between them it is not infinity because it has limits, i.e. 0 and 1 the universe, however has no such limits.

 

[drag]

Greetings !

Originally posted by Stormy
Ah, but that is the difference between the
mathematical and physical point of view.
In maths you have to have a starting point
and an end point, e.g. 0 and 1 but even
though there is an infinite number of
values between them it is not infinity
because it has limits, i.e. 0 and 1 the
universe, however has no such limits.

Perhaps the Universe is the result of two opposing
rules or something - this will allow a similar
situation on an appropriate physical scale.

Originally posted by Mentat
This is what drag, and others, keep saying,
but I disagree. If someone speaks of the
spacial dimensions themselves as expanding,
then it doesn't follow that just some things
could be getting farther apart, but all
things should be getting farther apart.
And if all things are getting farther apart,
then this has to be happening throughout the
entirety of space. Of course, there is not
"entirety of space" in an infinite universe,
which is why I don't think that everything
can get farther away from everything else,
in an infinite universe. Thus, the spacial
dimensions cannot expand, in an infinite
universe, IMCO (in my current opinion).

Actualy, I believe we WERE speaking of the whole
"deal" and everything in it, otherwise it's just
a local kind of expansion.
I do not understand the part about the "entirety
of space", what do you mean ?

Originally posted by wimms
Ah, now I'm lost. Why did you find important
to object that so strongly?

Because you seem to use a law that is only
recognized so far in the Universe to justify
the Universe itself or something "outside" of
what we currently call the Universe.
For all we know the Universe may've just appeared.

Originally posted by wimms
In regards to rings, what you mean by ring?

I was just trying to demonstrate that even for
a finite Universe there is NO "nothing" that
you can talk about because nothing is just
not anything. Mentat's thread dealt with this
in the past and I think this was a well justified
explanation. Anyway, my demonstration is that of
all of the 4 dimensions currently known to us.
Think of all of them as curved into rings - then
they have no defined bounderies beyond which you
could say there is something/nothing/whatever.

Originally posted by wimms
Universe not logical? kidding right? Some argue
that universe is not only logical, but rather
IS the thing itself.

I'm talking about the Paradox of Existence.
Our "logic" is the result of trying to understand
the way existence (the Universe) works, but there
are countless possibilities for it because we
may have infinite rules and complexity. Either way,
the rules of the game do not explain the existence
of the game (and that is the ALMOST absolute fact ).

Live long and prosper.

 

[wimms]

I've never implied one should think of nothing in any other way.

Originally posted by Mentat
Oh really?

By definition, beyond these boundaries theremust be Nothing. Now ponder for a moment, what is Nothing?

Come on, why are you doing this? Exactly next sentence is exactly what you are trying to put through.

Say you have two things separated by Nothing, not space, not stuff, not anything.

Please don't catch me on wording. English is my 3rd language afterall. Later I said enough to be unambiguous.

Originally posted by drag
Because you seem to use a law that is only recognized so far in the Universe to justify the Universe itself or something "outside" of what we currently call the Universe. For all we know the Universe may've just appeared.

no-no. I've never implied there is any "something outside universe". However bad my english is, its not that bad. I merely pointed out that based on our fundamental law of energy conservation, universe could not have been created or get destroyed. Universe is just bunch of energy afterall. If that law doesn't hold, then we have some tough days ahead. If there was a point when energy was created, then this law is flawed. What happened once, can happen again... Energy cannot be created "inside". If so, then it had to be created all in instant by something outside. I went on specifically to show that there can be no outside, from logical point of view, not some conventional belief. If there is something outside, its included by our definition of universe, and only question subject shifts - what created that outside? We, as being inside that universe obviously obey laws of the whole, are part of the whole.
You see, there is yelling contradiction between energy conservation law and concept of creation, byitself or by anything outside. If it just appeared from nothing, then anything can appear just from nothing, and there is no place for energy conservation.

I was just trying to demonstrate that even for a finite Universe there is NO "nothing" that you can talk about because nothing is just not anything. Mentat's thread dealt with this in the past and I think this was a well justified explanation. Anyway, my demonstration is that of all of the 4 dimensions currently known to us. Think of all of them as curved into rings - then they have no defined bounderies beyond which you could say there is something/nothing/whatever.

We've been talking about the same Nothing/not anything. I'm amazed how it could get confusing.

In regards to curved space, disagree. We can't escape the boundaries by means of intertial motion, but that has nothing to do with boundaries or what's beyond them. Curving space doesn't mean there are no boundaries, its just comfortable way to say that we can't care less of the rest. To get "unbounded" curved space we do what? We take finite boundaries and curve them onto themselves.
We can't escape BH, but beyond it is this same universe, over and over, without limits. It might be different, have even different laws, but its still same universe. You've basically suggested that Universe is kind of BH. I don't think so, BH is just a subset of universe, its finite.

Regarding "logic", agree, but I'd go further and say its result of not only us trying, but direct correspondence with the thing itself. So there are not so countless possibilities, they are not here.
Rules of game do not explain the existence of game, unless, the rules IS the game.

 

[Royce]

The universe whether flat, infinite, or curved, open, saddle back, or closed, sphere, is a sum zero game. All normal energy and matter is positive energy. Gravity is negative energy and the sum is equal or nearly egual to zero.
There are thoughts that our universe may be a local temporary disturbance in the vacuum, a vertual particle that because of inflation has not yet gone back into the vacuum from which it came. There is also the possibily that it is a singularity that grew massive enough to just close its local spacetime about itself thus "dropping" out of its universe/spacetime reference into a void without reference and has since expanded. It is also possible that God said "Let there be light." We can never know at, least in this life, because as the universe has expanded faster than the speed of light, at least in the inflationary phase the origin, and Big Bang is outside our light cone, beyond the limit of our sight.
To say that space is curved has been proven time and time again. It is the effect of mass/gravity that curves space. The question is, is there enought mass in the universe to close space completely and thus some billions of years in the future the expansion will be halted by gravity and then the universe will begin deflating back eventually into the singularity from which it all started, the Big Crunch. All of this implies that the universe is not infinite, has had a beginning and will have an end and may start the cycle all over again. There is no way of knowing if we exist in the first, last or hundredth cycle as the singularity destroys all information of anything if there was anything before it occured.

 

[plus]

Originally posted by Mentat
This is what drag, and others, keep saying, but I disagree. If someone speaks of the spatial dimensions themselves as expanding, then it doesn't follow that just some things could be getting farther apart, but all things should be getting farther apart. And if all things are getting farther apart, then this has to be happening throughout the entirety of space. Of course, there is not "entirety of space" in an infinite universe, which is why I don't think that everything can get farther away from everything else, in an infinite universe. Thus, the spatial dimensions cannot expand, in an infinite universe, IMCO (in my current opinion).

It needs to be defined relative to what, the points are getting farter apart from.

Clearly it can be measured that the stars are getting further apart using conventional measuring techniques. This is what people mean when they say that the universe is expanding. In the same way that I can move further away from this computer for ever, stars can move further away for ever. If you like, it could be measured relative to the speed of light.

 

[Mentat]

Originally posted by wimms
Come on, why are you doing this? Exactly next sentence is exactly what you are trying to put through.
Please don't catch me on wording. English is my 3rd language afterall. Later I said enough to be unambiguous.

No, no, your problem is still conceptual, not lingual. You use terms such as "seperated by nothing, not space, not stuff, not anything". This should mean that they are not seperated, but you still use the term "serperated by nothing". Did you mean that they weren't serperated?

BTW, I'm sorry if I offended you, by my intolerance of misuse of the word "nothing". I just hate that there are so many people who don't understand that the word "nothing" doesn't describe anything. You seem to understand that, and I commend that. Your third language? Which other two do you speak? (English is my second language, as I first spoke Spanish).

 

[wimms]

Originally posted by Mentat
No, no, your problem is still conceptual, not lingual. You use terms such as "seperated by nothing, not space, not stuff, not anything". This should mean that they are not seperated, but you still use the term "serperated by nothing". Did you mean that they weren't serperated?

Eh, infamous Nothing. You can't even explain that you "can't separate by nothing" without getting caught Of course I meant no separation.
I hope though that my main point finally got through, that in same way as you can't separate by nothing, you can't surround by nothing. Infinite unboundedness is thus the only possibility.
I speak estonian and russian. would survive with finnish.

 

[drag]

Greetings !

Originally posted by wimms
Please don't catch me on wording. English is
my 3rd language afterall.
...
However bad my english is, its not that bad.

It's my 3rd language too, and yours is very
good indeed.

Originally posted by wimms
Regarding "logic", agree, but I'd go further
and say its result of not only us trying, but
direct correspondence with the thing itself.
So there are not so countless possibilities,
they are not here.

Actually, it doesn't really work (in its "normal"
version) according to the "thing itself" as far as
we know it today.

Originally posted by wimms
Rules of game do not explain the existence of
game, unless, the rules IS the game.

That is a possibility but does not explain
their existence either, does it ?

Live long and prosper.

 

[RuroumiKenshin]

Originally posted by wimms
Eh, infamous Nothing. You can't even explain that you "can't separate by nothing" without getting caught Of course I meant no separation.
I hope though that my main point finally got through, that in same way as you can't separate by nothing, you can't surround by nothing. Infinite unboundedness is thus the only possibility.
I speak estonian and russian. would survive with finnish.

Mentat began a thread on the semantics of nothing. It lasted about 10 pages, if I recall correctly. Nothing means "not anything" therefore saying 'this is sepereted by nothing' is actually 'this is separated by not anything'. Are you getting "nothing" confused with a void??
If you meant no seperation, what did you mean?
English is my second language. (almost my third) The point is not how many languages you speak, its your understanding.

 

[drag]

Greetings !

Originally posted by wimms
I hope though that my main point finally got
through, that in same way as you can't
separate by nothing,

Perhaps, you're right. (Though I ussualy dislike
nearly absolute claims.)

Originally posted by wimms
you can't surround by nothing.
Infinite unboundedness is thus the only possibility.

That's an interesting logical deduction, but
I believe that other reasoning lines considered
it seems more like a semantic argument to me on
how much logical induction is present in it.

Live long and prosper.

 

[Michael F. Dmitriyev]

Originally posted by damgo
... But back to the original question...

When we talk about the expansion of an infinite universe, we don't mean its "total size" gets bigger in the way, say, a balloon gets bigger as we blow it up. We mean that the distances between objects in the infinite universe gets larger. So if there are originall objects at {..,-2,-1,0,1,2,...} they will move to {...,-4,-2,0,2,4,..} after some time, and continue to get further apart.

And hereinafter : BB
{..,-8,-4,0,4,8,..} ... ...
{..,-16,-8,0,8,16,..} ... ...
{..,-32,-6,0,16,32,..} ... ...

And the universe became the blowed balloon, which concentrated a whole matter in the shell.
Is it so?

 

[wimms]

Originally posted by wimms
Rules of game do not explain the existence of game, unless, the rules IS the game.

Originally posted by drag
That is a possibility but does not explain their existence either, does it ?

Yes, but it is interesting boundary situation that brings us to the limits of logical reasoning. Going past that will cause a short-circuit.

Think, what will remain after you "remove" all, mean ALL, from existence? To think about that, you need to apply logical reasoning. Say you conclude that what remains is nothing, oops, -> nothing remains. Just suppose, that we can imagine such condition. Then, we go on and apply logical reasoning. Or, frankly, we assert that logic remains. But logic is rules of a game, thus, if logic remains, it means existence remains. If you remove logic, you remove rules, and there is no game. Thus, rules of game and game are congruent, selfexplanatory, selfreferential. Asking anything beyond that point is invalid by ANY system of logical reasoning. Logic disintegrates.

By any system of logical reasoning, nothing is invalid state, not just impossible, but logically flawed concept. It may be "agreed" as impossible by reduction ad absurdum.

We have plenty of evidence that universe is logical, and very little evidence if at all that its absurd.
Therefore some believe that logic IS the game, rather than what it has or does. See http://ebtx.com for an interesting example.

 

[drag]

Originally posted by wimms
Yes, but it is interesting boundary situation
that brings us to the limits of logical
reasoning. Going past that will cause a
short-circuit.

Think, what will remain after you "remove"
all, mean ALL, from existence? To think
about that, you need to apply logical
reasoning. Say you conclude that what
remains is nothing, oops, -> nothing remains.
Just suppose, that we can imagine such
condition. Then, we go on and apply
logical reasoning. Or, frankly, we assert
that logic remains. But logic is rules of
a game, thus, if logic remains, it means
existence remains. If you remove logic, you
remove rules, and there is no game. Thus,
rules of game and game are congruent,
selfexplanatory, selfreferential. Asking
anything beyond that point is invalid by
ANY system of logical reasoning.
Logic disintegrates.

Precisely the point of my statement.

 

[Michael F. Dmitriyev]

Much varieties of infinity is considered in a philosophy and in mathematician. The Physics tries to find one in which is realized our universe. It is correct. God had chosen for realization one of them and this means that a rest infinityes are just result of creative fantasy of people and have no relation to realities.
Any project for realization must provide such features of the object:
- it must be a most simplicity upon a conservation of all functions;
- an expenseses of energy for its operation must be a minimum;
- it must function in "real time mode" for what must be an instant feedback and a compensating influences;
- it must have a most compactness for a minimization of amount of the elements for realization purpose required;
- no a possible changes of parameter in the system must not bring about its destruction;

Certainly nobody can not know all planning of God, but list of the requirements above for a more or less complex system is known to any designer. So. The Project is approved and its realization began .

Suppose this BB and the following expansion of universe.
But this is a full ignoring of project or, more exactly, its
straight opposition. Only Devil could realize such a project which destroy all planning of God. Herewith his force must be enough to work the system, which can't be working in principle. Anyway, his force might has been enough to inspire the Illusion to realization of such project to people.
It is possible to write this so
(The Absolute zero---> 3D number(?)) * INFINITY--->3D SPACE INFINITY.
This INFINITY of the EXPANSION of THREE- DIMENSIONAL SPACE.
This is the "acting model of our universe".

Really, it is required a superconcepts and huge amount of subterfuges to present working of such "universe". Nobody can't to do it.

What must be a realization to corresponds on the minimum set of the requirements, at least?

It must be the EVOLUTION toward a certain ABSOLUTENESS, but must not BULGE SENSELESSLY in their own size to NOWHERE.
It must not achieve this ABSOLUTENESS in principle and it provides the INFINITY of the PROCESS of EVOLUTION.

Mathematically, this requirements correspond to the process of the endless fission of any real number which will not reach the ABSOLUTE ZERO never.

NUMBER / INFINITY ------> ABSOLUTE ZERO
This is a REAL INFINITY.
This is ALGORITHM, not formula, since a Number has a BINARY FORM. GOD from the beginning had used the INFORMATION DIGITAL TECHNOLOGY.
Physically this process must have a FUNDAMENTAL ESSENCE presenting a number in mathematical model.
This the essence is TIME!

Michael F. Dmitriyev

 

[wimms]

-- in same way as you can't separate by nothing, you can't surround by nothing.

posted by drag
That's an interesting logical deduction, but I believe that other reasoning lines considered it seems more like a semantic argument to me on how much logical induction is present in it.

Seems? Show me the flaw. And, while at that, how does BB get away from that?