Calculating the probability that the Universe is finite

[PeterDonis]

The summary that immediately follows the title of this thread.

Then no, your edit is not correct. I explained why in post #57.

 

[Buzz Bloom]

Then no, your edit is not correct. I explained why in post #57.

Hi @PeterDonis:

I read Post #57, and I thought I had captured the relevant assumptions in the three I put into the summary. Please tell me specifically which of the three I put into the summary are wrong, and which of your comments in Post # 57 are necessary for me to describe in the summary since they are the relevant assumptions to the meaningfulness of the probability calculation for finiteness.

Regards,
Buzz

 

[PeterDonis]

Please tell me specifically which of the three I put into the summary are wrong

I already told you in post #57. Specifically, the fifth quote from you in that post and my response to it. My response explains why assumption #3 in your revised summary is the wrong assumption.

 

[Buzz Bloom]

No, it is based on the assumption that Ωk is a free parameter, to be estimated from the data, so it is possible in principle for it to have any value consistent with the data.

The mathematical fact I was trying to address by assumption 3 is that any particular value has a zero probability. It is possible to calculate a non-zero probability for a range of values, but not for a single value. A flat universe requires that Ω_k is exactly zero. A finite hyper-spherical universe can have any value of Ω_k greater than zero. An infinite hyper-hyperbolic universe can have any value of Ω_k less than zero. This is why I read your comment #5 as not an assumption, but a conclusion that the probability of flatness is zero given the three assumptions I made.

If I need to phrase my assumption 3 better, please advise me.

Regards,
Buzz

 

[PeterDonis]

The mathematical fact I was trying to address by assumption 3 is that any particular value has a zero probability.

Yes, but that holds for every value in the distribution, not just $\Omega_k = 0$. So this "fact", if you take it literally, means that every possible value for $\Omega_k$ has zero probability, hence $\Omega_k$ cannot have any value at all. So this "fact" cannot possibly mean what you are asserting it to mean.

This is why I read your comment #5 as not an assumption

Then you read it incorrectly.

If I need to phrase my assumption 3 better, please advise me.

I already told you how to phrase it, in the specific part of post #57 that I already drew your attention to.

 

[PeterDonis]

This is why I read your comment #5 as not an assumption

Even though I explicitly used the words "based on the assumption that..." followed by the assumption. I don't see how I could possibly be any clearer that I was stating an assumption, and since that statement was immediately preceded by "No" in response to your statement of an assumption, I don't see how I could possibly be any clearer that I was correcting your statement of the assumption.

I think you are making this a lot harder than it needs to be. I think you need to stop trying to over-interpret what others are saying and pay more attention to the actual words being used.

 

[PeterDonis]

A flat universe requires that Ω_k is exactly zero. A finite hyper-spherical universe can have any value of Ω_k greater than zero. An infinite hyper-hyperbolic universe can have any value of Ω_k less than zero.

Even leaving aside the issue I raised in post #65, what you're describing here isn't an assumption, it's a logical argument. But what you wanted to put in the summary for this thread was assumptions, not logical arguments. The assumption that this logical argument is based on is still the one I stated in post #57, not the one you put in assumption #3 of the summary when you edited it.

 

[PeterDonis]

a conclusion that the probability of flatness is zero given the three assumptions I made

The third of your assumptions says that the probability of flatness is zero. So you can't conclude from it that the probability of flatness is zero. You already assumed it directly.

 

[Buzz Bloom]

Hi @PeterDonis:

I am quoting my assumption #3 together with your reading of it.

The third of your assumptions says that the probability of flatness is zero.

My #3
(3) that the universe is not and cannot be flat.

My assumption (3) needs to be rewritten because my intention is to make clear the assumption that the probability that the universe is flat is zero. My carelessness led me to what I wrote, and it does not say that, and it is in fact an error.

If I wrote the assumption (3) as: the probability that the universe is flat is zero, would that be OK?

Regards,
Buzz

 

[PeterDonis]

If I wrote the assumption (3) as: the probability that the universe is flat is zero, would that be OK?

No. The assumption is what I said in post #57 in response to this. I have already said so. More than once.

The statement in bold above is a conclusion, not an assumption--and, as I have already said in post #65, the logical argument you are using to get from the actual assumption being made (the one I stated in post #57 in response to the fifth quote from you in that post--I'm not going to quote it here since you have had more than enough time to go back and read what it actually says, which it appears you haven't done since you are unable to correctly state what it actually says) is questionable.

But regardless of the status of that logical argument, it is a logical argument, and the assumption you should be stating is the point from which that argument starts, not the point at which it ends. The end of a logical argument is not an assumption, it is a conclusion.

 

[PeterDonis]

And with that, this thread is closed. @Buzz Bloom you can PM me if you have further questions about what I have said. We have beat this topic more than enough for a public thread.