Largest Galaxy In An Infinite Universe

[Hornbein]

Let's suppose that the universe is infinite and the size of galaxies is normally distributed. Then there is no largest galaxy. Conclusion : the size is not normally distributed.

The same is true for any distribution that has a positive probability for all possibilities. So that can't be the case. All that is left is some distribution that has a maximum possible size. In this case there will still be no largest galaxy. Instead there will be galaxies approaching this limit in size but never reaching it. No matter how close a galaxy comes to the limit there will always be a infinitesimally larger galaxy.

Or is this true? In an infinite universe there could be a great many galaxies of probability zero that are larger than the limit. But the chance that Earthlings would ever observe such a galaxy is also zero so it is of no practical interest. Then again it is possible that there truly is a hard limit and a galaxy with diameter greater than X is impossible. But as noted before, that doesn't mean that there is a galaxy of maximum size.

 

[DaveC426913]

No matter how close a galaxy comes to the limit there will always be a infinitesimally larger galaxy.

How does this follow? Why does there have to be some larger galaxy?

I think one of the problems here is that you can never know what some hypothetical maximum limit might be. There's just a bunch of galaxies distributed on a curve. The graph is infinite in extent, but that does not mean there have to be data points beyond some given point down range.

Oh, I see - you put the constraint on it that it is normally distributed.

OK, but surely that does not have to hold at the leaky margins where the number of galaxies might have to be fractional. (i.e. instead of n galaxies per gigaparsec, you have to start saying n gigparscecs per galaxy or 1/nth of a galaxy per gigaparsec).

Being described as a 'normal distribution' is only nominally true, right? It's not true at all levels of scrutiny, right?

(It's fairly apparent that I am not schooled in statistics and its terminology, but I think I intuit the issues.)

 

[Hornbein]

How does this follow? Why does there have to be some larger galaxy?

I think one of the problems here is that you can never know what some hypothetical maximum limit might be. There's just a bunch of galaxies distributed on a curve. The graph is infinite in extent, but that does not mean there have to be data points beyond some given point down range.

In a finite sample that is true, but with an infinite sample and a distribution like the normal then the probability that there is a point with value greater than X is always one.

In practical terms even here on finite Earth there is no such thing as something that is normally distributed. It's always an approximation. Usually there is a hard limit in at least one direction. There will never be a person whose height has a negative value, even in an infinite Universe. But since everything is an approximation of normal there is no need to mention it.

One of the points is that when we are dealing with something that really is infinite then there is a distinction between probability zero and something that is impossible. There is also a distinction between probability one and something that is an absolute certainty.

 

[DaveC426913]

Right, so it sounds like you've second-guessed yourself and arrived at an answer. True? Or has it spawned a new question? Can you reformulate that new question?

 

[Hornbein]

Right, so it sounds like you've second-guessed yourself and arrived at an answer. True? Or has it spawned a new question? Can you reformulate that new question?

These are just rhetorical questions and wandering musings about the weird stuff that arises when you hypothesize infinite spaces with infinite sample sizes.

 

[Vanadium 50]

Oh boy.

This starter is filled with a ton of misconceptions. Picking at them oine by one is probably inefficient, so let's get to the heart of the issue: please define "galaxy" and explain how to determine it's "size".

 

[Hornbein]

Oh boy.

This starter is filled with a ton of misconceptions. Picking at them oine by one is probably inefficient, so let's get to the heart of the issue: please define "galaxy" and explain how to determine it's "size".

Since as far as we know it is impossible to observe anything outside of the visible Universe we are already in a theoretical mathematical land. So we are assuming that all such physics difficulties are solved by some futuristic superscience combined with arbitrary standards.

 

[Ibix]

So we are assuming that all such physics difficulties are solved by some futuristic superscience combined with arbitrary standards.

You can't just pretend definitions don't matter. Would a true FLRW universe everywhere filled with a uniform density fluid that never collapses because there are no non-uniformities count as a single galaxy to you? Or do you need stars?

 

[Hornbein]

You can't just pretend definitions don't matter.

In math you can wave your hand and remove all such difficulties. I say that these are not the interesting parts of the matter.

If you want to rule that this is a physics site, not math, so this is all off topic that's fine with me. I may have been unwise in starting this thread in the first place. But I have noticed physicists opining on probabilities in an infinite universe....

 

[Vanadium 50]

You can declare that this is math and not physics (although one can be forgiven for concluding the reverse since this is a physics section of a physics forum). Or you can declare that definitions are unimportant.

But you can't do both.

 

[Ibix]

In math you can wave your hand and remove all such difficulties. I say that these are not the interesting parts of the matter.

Ok. Then obviously there's no limit to the maximum possible size beause of the previously mentioned example of a perfect FLRW universe, filled everywhere with a single uniform fluid galaxy.

 

[BWV]

Many things in nature are distributed by power laws, not a normal distribution - earthquake strength, volcanic eruptions, size of stars

same with every day life - sample the wealth of 1,000,000 people on the planet and then try to calculate the probability of Elon Musk's net worth

 

[Vanadium 50]

single uniform fluid galaxy.

This is why I wanted (and failed) to get a definition out of the OP. Somehow I get the feeling he would say "No, that doesn't count."

My thinking was in a different direction. A galaxy is not just a bunch of stars. It is a gravitational bound aggregate. So what does it mean for two stars not in each other's visible universe to be gravitationally bound to each other? I had hoped he would give us a definition of a galaxy that could possibly be bigger than the visible universe.