Extent of space (APOD 23 Mar 2006)

[bystander]

Infinity means without boundaries. It is said there is no edge of the universe (no boundary). So, by definition, isn't it infinite?

To say the set of integers is countably infinite is the same as saying there is no largest integer. You can't count them all because there is always one more to count. This is not a limit, it is the lack of one.

Anyway, any implication about the limits of the universe, real or not, implies nothing about the reality of the universe as a whole.

Dr. Skeptic, I strongly suspect there is a fallacy in your previous logic. Having slept a couple of times since I studied logic, I can't point them out, but your arguments arouse the skeptic in me.

[tbg10101]

Mathematically speaking, the only set of problems that can include infinity as te product must have infinity as the basis.
Infinity (I)
I+I=I
I-I=I
IxI=I
I/I=1
Otherwise the product of any whole number will be just another whole number.

There are no 2 whole numbers whose product = I

That's too general. Yopu can also do this:

I/I=I
(2*I)/I=I
(2*(I/I))/(I/I)=I
Cancel out I and you get 2=I

Infinity is not one huge number. It is EVERY number.

[jackr]

Dr. Skeptic's repeated rush to declare things "meaningless," seems related to his:

Empirical data cannot reach the limit of infinity. Remember, infinity is a (non?) limit not a number.

not to mention his signature:

Speculation ≠ Science

That is: "Science" is "empiricism," which is "actually going out and counting things". I think that's a reasonable definition of "science," and it reasonably leads to claims like "there is no infinity in science."

But that's not what he says. He says "there is no infinity in the universe." This requires the bold assumption "there is no universe outside of science," an assumption we have not yet seen justified in this thread, and which, actually, I'm not personally prepared to make.

And again, this is related to the disclaimer posted by Nereid, much earlier in this thread,

That the 'big bang' is some kind of explosion, from a point somewhere in space, is one of most common misconceptions; see, for example, this page for more detail.

A summary of the discussions linked from that disclaimer is something like "The Big Bang Theory says some things about the current universe, and the past universe, and that is all. Extrapolating these things backwards to indicate an 'exploding point' origin is beyond the science." This Zeno's-paradox meaningless infinity business seems a similar unjustified extrapolation. Quantum theory says some pretty surprising things, but some of the most surprising have been confirmed, and need to be taken as science at least until some fancier theory can explain both them and our familiar experience. But quantum theory itself does not extrapolate to the realm of "infinity"; that is going beyond valid realm.

[Qev]

Infinity means without boundaries. It is said there is no edge of the universe (no boundary). So, by definition, isn't it infinite?

Not necessarily. The universe can be 'boundless, but finite'. A decent two-dimensional analogy is the surface of a sphere. It has no boundary (you can never encounter an edge while your motion is confined to the two-dimensional surface), and yet it has a finite surface area.

I suppose infinity is non-empirical, in that it's not actually measurable in any finite sense, but that doesn't necessarily make it unscientific, I don't think? It may be immeasurable, but it's not nondisprovable.

[Dr. Skeptic]

But that's not what he says. He says "there is no infinity in the universe." This requires the bold assumption "there is no universe outside of science," an assumption we have not yet seen justified in this thread, and which, actually, I'm not personally prepared to make.

Let me clarify, there is no infinity in the empirical universe. If math/physics progresses where that is no longer true, I'll stand in wonderment and bid farewell to quantum mechanics and the Planck Length.

Also let me reiterate, infinity is not a number, it is not an empirical unit, it is a non-limit that shouldn't be confused with being an integer.

[NoelC]

There is most certainly a largest number.

Not in the way you think I mean, however.

Just because one *can* count to a number one higher, doesn't mean that anyone has.

Somewhere, sometime, someone has published the largest number ever expressed. This is a finite, specific value. Until someone represents a larger value, that one stands as the largest number. I have no idea who or where or what that number is.

My point is, here, that we may all try to imagine infinity, yet anything we have ever expressed or CAN express is still yet a finite value.

If we lined up the bytes in all the computer memories in the whole world and called that a number, it is very large indeed, yet still finite.

Very large does not equate to infinite. It does not even hold a candle to it.

In Engineering we often represent things as "undefined" rather than "infinite". For example, the value of x/0 is typically called "undefined". I like "undefined", personally, because it tends to not invite the reader to try to imagine a really big value.

If we lined up the atoms in all the universe...

But wait, is there such a thing as "all the universe"? I don't think anyone knows. Yet in the blink of an eye we might imagine the whole universe as a little sparkling ball.

Robert Heinlein may have touched on the subject a bit: "Thou art God"

-Noel

[goredsox]

Quoting NoelC:

Somewhere, sometime, someone has published the largest number ever expressed. This is a finite, specific value. Until someone represents a larger value, that one stands as the largest number. I have no idea who or where or what that number is.

I'll take a stab at that. How about a googolplex raised to a googolplex power, and then the result raised to a googolplex power, etc, a googolplex times? (errr..... plus one.)

In other words, can it be said that expressions of very large integers can get to the point of the absurd, even well before the infinite?

[Dr. Skeptic]

There is most certainly a largest number.

Not in the way you think I mean, however.

Just because one *can* count to a number one higher, doesn't mean that anyone has.

Somewhere, sometime, someone has published the largest number ever expressed. This is a finite, specific value. Until someone represents a larger value, that one stands as the largest number. I have no idea who or where or what that number is.

My point is, here, that we may all try to imagine infinity, yet anything we have ever expressed or CAN express is still yet a finite value.

If we lined up the bytes in all the computer memories in the whole world and called that a number, it is very large indeed, yet still finite.

Very large does not equate to infinite. It does not even hold a candle to it.

In Engineering we often represent things as "undefined" rather than "infinite". For example, the value of x/0 is typically called "undefined". I like "undefined", personally, because it tends to not invite the reader to try to imagine a really big value.

If we lined up the atoms in all the universe...

But wait, is there such a thing as "all the universe"? I don't think anyone knows. Yet in the blink of an eye we might imagine the whole universe as a little sparkling ball.

Robert Heinlein may have touched on the subject a bit: "Thou art God"

-Noel

In an empirical sense the largest number would be the number of Planck lengths in the universe, in conceptual numbers there is no limit - so we invented the infinity (non)limit. Infinity is conceptual and not empirical.

[bystander]

There is most certainly a largest number.

Not in the way you think I mean, however.

Just because one *can* count to a number one higher, doesn't mean that anyone has.

Somewhere, sometime, someone has published the largest number ever expressed. This is a finite, specific value. Until someone represents a larger value, that one stands as the largest number. I have no idea who or where or what that number is.

-Noel

I disagree. Let's take your largest number. I don't need to know how it is expressed. Let's just call it n. I can now express a large number (an infinite number?) of terms larger than your number. (n+1), (2n), etc. So, before you even expressed your largest number, I have expressed some that are larger.

This is just mathematics. It says nothing about my imagination or lack thereof. To say something is countable is mathematics, also. A set is countable if that set can be transformed or mapped into the set of cardinal (counting) numbers.

Integers are countable. We have positive integers (essentially the cardinal numbers), negative integers (easily mapped), and zero.

Even rational numbers are countable, and there is an infinite number of them between any two integers. Since a rational number can be expressed as a ratio of integers, they can be mapped to the set of cardinal numbers.

Real numbers are not countable. At least I don't know of any way to map all real numbers to the set of cardinal numbers.

[NoelC]

I think you may actually be agreeing with me, bystander.

As well put by the others, there's empirical and there's conceptual. "Infinity" is conceptual, as is "Undefined". So is N+1.

Is there a defined or infinite size to the universe? We may never really know, and somehow that feels wrong.

Is there a minimal expression of time (e.g., one cycle time in this wonderful complex computer simulation we all live in)? Sure would like to have that processor my desktop.

-Noel

[marion ballantyne]

[quote="Dutchman"]So what's everyone's opinion on the extent of the universe? Finite or infinite?[/quote]
Suppose expansion does not stop it means that everything will continue to move further apart, galaxies, clusters etc.
In this universe, the stars will use up the hydrogen fuel that powers them, and the glowing stars become fewer and fade, and the universe fizzles out.
One theory - maybe a possibility?

[NoelC]

If, in the ultimate sense, matter and energy are interchangeable, then isn't it possible a civilization will learn to convert one to the other?

Assuming that civilization can continue until all locatable matter is turned into energy, which dissipates by radiating outward, what then? Is all that energy coalescing back into a shell of matter around the "outside" of the Universe? Or falling into black holes? Is the ultimate memory of all the glory of the universe just a dim afterglow?

Would one find oneself a part of a whole 'nother sub-universe if one were inside the event horizon of a black hole? Which direction does time flow in there?

-Noel

[makc]

I think what DrSceptic was saying is this: whenevr we measure the size (the <whatever>) of the universe, we always end up with a number, and since it is a number, it can never be infinite.

Well, there are ways to resolve this. We simply need include infinity in our set of numbers. Details on two common ways of doing so can be found here and here.

[kovil]

1. Is the universe infinite or finite?

2. Where does the space come from that the universe is expanding into, if it is indeed expanding, and if not expanding, where did it come from to begin with?

3. How did the universe start and how will it end?


1. In Western Philosophy 'either/or' is a favorite posit of exposition.
In Eastern Philosophy 'both/and' is the favored posit of resolution.
Could it be that the Universe is both finite and infinite?
Finite to the extent of the Universe of which we can ever have an awareness of, and infinite to the extent of the Universe of which we will never have any awareness about.
Would this make the Universe subjective by awareness, and objective by inference?

2. Here on Earth, and for as far as we can see, both in the large and in the small; things happen by Transformational Causation. One thing transforms because of some other action, cause, event, change etc.
The primal causation of the Universe cannot be by transformational causation, one thing changing into something else. It must be by Apparitional Causation, meaning the Universe arose from something not of this universe. We know not what that something was, but it was not something of this universe. That something not of this Universe is also what lies beyond this Universe, and that is what this Universe is expanding into, if indeed it is expanding.

3. As John Dobson likes to describe it, This Universe is like a moving picture show, we came in somewhere after the start and we will leave before the end, we only get to see that part of the show while we are here.


btw, I very much enjoyed this topic and all the great posts on infinity! Well done, and thanks very much!

[Dr. Skeptic]

I think what DrSceptic was saying is this: whenevr we measure the size (the <whatever>) of the universe, we always end up with a number, and since it is a number, it can never be infinite.

Well, there are ways to resolve this. We simply need include infinity in our set of numbers. Details on two common ways of doing so can be found here and here.

Adding infinity as an integer? Do you really want to open that can of worms?

[makc]

it's better than limiting possible answers a-priori.

[Dr. Skeptic]

it's better than limiting possible answers a-priori.

Is it?

[NoelC]

Isn't that just the debate here?

If the universe is infinite, then there is no integer that can be used to express its size.

If the universe is finite, it's still bigger than we could ever hope to measure, but at least we can put a number on it and be comforted by the knowledge that we are not infinitely insigificant, just extremely so.

-Noel

[Dr. Skeptic]

Isn't that just the debate here?

If the universe is infinite, then there is no integer that can be used to express its size.

If the universe is finite, it's still bigger than we could ever hope to measure, but at least we can put a number on it and be comforted by the knowledge that we are not infinitely insigificant, just extremely so.

-Noel

It think we have covered this before and how hard it is to grasp how large infinity really is.

If the universe and/or time were infinite, it would allow the mathematical statement "1/infinity" to be real value. The result would be any possible event would have to have taken place because the probability of any event would be equivalent to infinity/infinity = 1 or 100%, even if/when events contradict each other.

[Chris Peterson]

If the universe and/or time were infinite, it would allow the mathematical statement "1/infinity" to be real value. The result would be any possible event would have to have taken place because the probability of any event would be equivalent to infinity/infinity = 1 or 100%, even if/when events contradict each other.

Not at all. Certainly, you can't use infinity in mathematical expressions as if it were a number. It isn't, and such logic is invalid. Infinity shows up mathematically when limits are used.

There is no highest integer, even on a number line that extends infinitely far. No matter how far you go, the Universe will continue to generate new, unique integers. The same can be true for events. Given the degrees of freedom provided by infinite space and/or infinite time, what makes you think that the number of possible events doesn't increase faster than the space/time needed to express them?

An infinite universe does not mean that the probability of every possible event is one.

[PassionateBomba]

Oh I agree, I agree!!!

But the argument has left the arena and is poured into the streets. The wondrous ponderings of the universe posed in the original post, has diminished to chaotic rock throwing riots of mathematical wizardry which answers are equivalent to, "how big can you build an abacus?"

The universe is finite by definition. No one can measure it so no one can know its volume. However, the universe by design is a product of thought. A question of how far can I go? Only to realize, you have gone nowhere and remain where you began. (You do not see a galaxy 50 million light years away, you see light that is here, right now.) Therefore, the universe is 10x our ability to think. Think as big as you can and multiply by 10. You can make that collective thought if you desire.

The answer is as simplistic as round's ability to roll. And just as round's ability to roll is governed by the rules gravity, mathematics, so are all things in the universe governed by the same rules, without which it cannot exist.
In conclusion, the universe is but a spec in comparison to its ruler and sustenance, Infinity.

Love
PB

[Dr. Skeptic]

If the universe and/or time were infinite, it would allow the mathematical statement "1/infinity" to be real value. The result would be any possible event would have to have taken place because the probability of any event would be equivalent to infinity/infinity = 1 or 100%, even if/when events contradict each other.

Not at all. Certainly, you can't use infinity in mathematical expressions as if it were a number. It isn't, and such logic is invalid. Infinity shows up mathematically when limits are used.

There is no highest integer, even on a number line that extends infinitely far. No matter how far you go, the Universe will continue to generate new, unique integers. The same can be true for events. Given the degrees of freedom provided by infinite space and/or infinite time, what makes you think that the number of possible events doesn't increase faster than the space/time needed to express them?

An infinite universe does not mean that the probability of every possible event is one.

Infinity is a conceptual limit, it does not exist passed our imaginations. Quantum mechanics states "Everything" need to be measured in quantum units, at a finite time there is a finite number of planck's lengths in the universe, multiply that number by 10 it remains an integer but is transposed into a conceptual number because it's value doesn't exist in the universe.

An infinite universe does not mean that the probability of every possible event is one.

Can you show me to logic this statement is based on?

[kovil]

Infinity ; what a concept.

If the Universe is infinite, would that then indicate that there is no God?
As how could God create something truly infinite, it would by definition be larger than its creator, a logical impossibility, when one is talking creatively.

If there is a God, then the Universe is finite.

Is this a good starting point? or does it confuse the issue?

[Case]

Infinity is a conceptual limit

More like the lack of a limit

Quantum mechanics states "Everything" need to be measured in quantum units

I see no reason why that should extend to "time" and "distance". Neither are objects made of particles.

it would by definition be larger than its creator, a logical impossibility

Not at all. Mankind constantly creates things larger than themselves.
Even with infinity this is possible: there are infinite numbers between 0 and 1, but there are numbers outside that range (e.g. "2"). Something infinitely large does not have to cover everything.

[Dr. Skeptic]

I see no reason why that should extend to "time" and "distance". Neither are objects made of particles.

Quantum Mechanics is not limited to particles, Space/Time and Mass/Gravity are interdependent values governed by quantum mechanics.

Its "All or None" when it comes to Quantum Mechanics.

That does include time, time cannot be infinite - it is required to have a starting point and an end point and must be composed of/by quantum units. Time is the fluid measurement of energy's propagation as it moves dimensionally across Planck's Lengths, (this is why Relativity works).

To over simplify the point, A Planck's Length is the smallest measure of distance, 1/2 of a Planck's Length does not exist. The String Theory states that its like a small loop on a string, moving off the string, Space/Time does not exist and cannot be measured. Empirical data is derived by what happens on the loops.