Is the Universe Infinite? Or is only God Infinite?

[Skyler]

Jonathan,
You are right that radiation received falls off with the square of distance, but with an infinite number of stars you would still get radiation from every point in the sky. Occultation by dark objects would not be sufficient as any radiation absorbed by such objects would necessarily have to be re-radiated by that object at some point due to conservation of energy.

This is true, but because the universe is composed of discrete units, and radiation sources are not mathematical points, "every point in the sky" still constitutes a finite set of radiation sources (albeit a large one).

For a simple analogy, consider a pixellated circle. From the center of the circle, you can draw a ray in any direction, but it will always intersect with one of a finite number of pixels.

 

[SRoper]

Steve,
If the universe was infinite in extent but had a starting point in time we would expect the radiation (light) reaching us to increase with each year.

This is an interesting observation. Does the argument also apply to universes which are finite but simply much bigger than what we have seen so far ... because of perhaps, inflation during the early moments?

(For those who don't know, some scientists have hypothesised that for a brief moment of time soon after the big bang, the universe underwent a period of "inflation", when it grew much faster than the speed of light. They suggest that not only is this theoretically possible, but that it would explain the "flat" nature of space - suggesting that it is much bigger than we have yet seen.)

I wonder if this argument fails because it also makes assumptions about the density of light sources in a possible infinite universe. In other words, perhaps this is happening, but we haven't been taking careful measure of the light reaching us for long enough for it to be noticeable, given the relatively low density of the universe.

I suppose its not so much an argument but, as you said, an observation as to what would necessarily happen. The scale of such an increase is certainly unmeasureable over the timescales we've been making observations. I believe the current understanding in cosmology is that the universe is expanding at an increasing rate such that the extent of the observable universe continues to be less.

Jonathan,
You are right that radiation received falls off with the square of distance, but with an infinite number of stars you would still get radiation from every point in the sky. Occultation by dark objects would not be sufficient as any radiation absorbed by such objects would necessarily have to be re-radiated by that object at some point due to conservation of energy.

This is true, but because the universe is composed of discrete units, and radiation sources are not mathematical points, "every point in the sky" still constitutes a finite set of radiation sources (albeit a large one).

For a simple analogy, consider a pixellated circle. From the center of the circle, you can draw a ray in any direction, but it will always intersect with one of a finite number of pixels.

I'm not sure I follow, but it seems to me the situation is analogous to randomly picking a real number between 0 and 1 an infinite number of times. Would you reach every point on the segment? I'm genuinely asking the question because I'm a little hazy on my math. Intuitively I want to say yes because the alternative is that you never reach some point P which would call into the question whether the probability density was truly uniform. I don't know. Weird stuff happens with infinity. I can say with confidence that the sky will appear to be uniformly white at any arbitrary resolution. To use my analog, there exists no interval [P1 P2] where 0 <= P1 < P2 <= 1 where you would not find a point that is in the infinite series of random points.

 

[Afterthought]

I'm not sure I follow, but it seems to me the situation is analogous to randomly picking a real number between 0 and 1 an infinite number of times. Would you reach every point on the segment?

Seems to me the picking forms a countable set, so no.


Is infinity an incommunicable attribute of God? Perhaps the "infinite" spatial extent is different from God's infinity?

 

[SRoper]

I'm not sure I follow, but it seems to me the situation is analogous to randomly picking a real number between 0 and 1 an infinite number of times. Would you reach every point on the segment?

Seems to me the picking forms a countable set, so no.

Ah, of course you are right, Raymond.

 

[Skyler]

I'm not sure I follow, but it seems to me the situation is analogous to randomly picking a real number between 0 and 1 an infinite number of times. Would you reach every point on the segment? I'm genuinely asking the question because I'm a little hazy on my math.

Mathematically yes; physically, the analogy would only apply if you could only pick numbers in increments, of, say, 0.001 - because there's a limit decreed by the minimum size of the radiation source.

 

[hammondjones]

Matter/energy may be discrete, but whether or not space-time is discrete is an open question, as far as I know. Even if there is a finite amount of matter in the universe, I don't think that it necessarily follows that the universe itself is finite. Perhaps, though, I am making an unwarranted distinction between the universe and the matter contained in it.

 

[SRoper]

It has nothing to do with the minimum size of the radiation source, rather it is the position of the radiation source in the sky relative to the observer (elevation and azimuth). As long as there is a nonzero chance of a radiation source in any given direction, there would be a source at every point in the sky resolved to any arbitrary resolution.

 

[Afterthought]

Is infinity an incommunicable attribute of God? Perhaps the "infinite" spatial extent is different from God's infinity?

I checked a few sources and yes, infinity is considered an incommunicable attribute. So now the question is: does this infinity differ from what we mean when we say the universe is infinite? Perhaps the difference is that God's infinity of being means that all of Him is everywhere, whereas for the infinity of space, the space just goes on and on, rather than all the space being everywhere?

 

[Skyler]

It has nothing to do with the minimum size of the radiation source, rather it is the position of the radiation source in the sky relative to the observer (elevation and azimuth). As long as there is a nonzero chance of a radiation source in any given direction, there would be a source at every point in the sky resolved to any arbitrary resolution.

Yes, but many of those infinite points in the sky would resolve to the same radiation source. Like the pixellated circle, you can draw rays in finer and finer increments, but they would still hit one of a finite number of pixels.

In other words, it's not the number of points in the sky; it's the number of unique radiation sources.

 

[The Conductor]

It is technically possible to be infinite without repeating oneself or doing everything.
Certain transcendental numbers, for example, contain only ones and zeroes. If one were to convert this into words via some arbitrary number-to-letter conversion, many, if not most words would not appear.

That being said, I don't believe that the universe is infinite, but it would only excite me if I found out it was. The sheer size of the universe compared to the size of the inhabited universe says a lot about God's sovereignty.

Job38:25-27 ESV
“Who has cleft a channel for the torrents of rain
and a way for the thunderbolt,
to bring rain on a land where no man is,
on the desert in which there is no man,
to satisfy the waste and desolate land,
and to make the ground sprout with grass?

 

[tommyb]

If the universe was infinite how could it be expanding?

 

[Brian Bosse]

Hello Everyone,

This thread could easily be in the philosophy section. When we speak of 'eternality' and 'infinity', what do we mean?

A set is defined to be infinite if it can be placed in one-to-one correspondence with a proper subset of itself.

When Steve speaks of the infinite in terms of the size of a set (its cardinality), he is using 'infinite' as a technical term. In this case, the context is some formal mathematical system - some set theory. As such, this definition is nothing more than a mathematical construct, and may or may not have anything to do with reality. To that end, when the Bible speaks of God being infinite, it would be a mistake to import this or some other meta-mathematical definition into the term. (Note: I do not think Steve was doing this. I think he simply was responding to someone else's question about how some mathematicians (not all) use the term 'infinity'.)

So, what does the Bible mean when it speaks of God's eternality? I think it is safe to say it has nothing to do with Cantor's paradise.

Sincerely,

Brian