The odds are one in an infinity

[bobsmith76]

If the odds of getting the right answer are one in an infinity, is it possible to stumble on to the right answer?

 

[micromass]

Could you please clarify your question??

 

[pmsrw3]

I'm going to rephrase your question a little: is it possible for an event with probability zero -- that's my translation of "1 in an infinity" -- to happen? The answer is yes. (At least, it is mathematically possible -- it's not completely clear that in the real physical world there is such a thing as a possible event with probability zero.)

All impossible events have probability zero. But not all probability zero events are impossible.

 

[HallsofIvy]

Yes- and thanks for rephrasing. I would never accept "1 in infinity" as a probability or, indeed, as meaning anything.

If your set of possible events is the set of numbers from 0 to 1, that is we are selecting a number from all numbers between 0 and 1, then the probability the number chosen is in subset A is the measure of set A. If set A contains only a single number (or any countable set of numbers) then its measure is 0 so the probability of choosing any specific number is 0. But, obviously when we choose a number that particular number is chosen.

It is only for discrete probability distributions that "probability 0" means "impossible" or that "probability 1" means "certain".

 

[bobsmith76]

Thanks everyone for the quick participation.

Let me try to explain how I got this question. I was trying to prove that the probabilistic space of the correct laws of physics arising out of nothing by chance was infinite, since nothing cannot be measured. For example, the Lambda constant must be tuned to one part in 120 orders of magnitude. It's not that the odds of chance tuning it correctly are one in 120 orders of magnitude, rather the odds are infinite because there is nothing to restrict the probabilistic space. However, it would also follow that the amount of probabilistic resources are also infinite, since if nothing exists, then that would include probabilistic resources.

So what are the odds of scoring the right item out of an infinite list, if you have an infinite amount of time to try? I guess the odds would be 1. But I would also like to know what the odds of scoring the right item is, if the list is infinite.

 

[pmsrw3]

For example, the Lambda constant must be tuned to one part in 120 orders of magnitude. It's not that the odds of chance tuning it correctly are one in 120 orders of magnitude, rather the odds are infinite because there is nothing to restrict the probabilistic space.

Well you don't actually know that, do you? This is an interesting question that every attempt to think about the probability of the universe runs into--it's called the measure problem.

So what are the odds of scoring the right item out of an infinite list, if you have an infinite amount of time to try? I guess the odds would be 1.

Any probability between 0 and 1 (inclusive) is possible. You need to specify more exactly what the infinite list is, what the probabilities of individual items in it are, what constitutes a right choice, and how you use the time. (Yes, I know it's infinite. There are still choices.)

But I would also like to know what the odds of scoring the right item is, if the list is infinite.

Once again, it could be anything from 0 to 1.

 

[chiro]

Thanks everyone for the quick participation.

Let me try to explain how I got this question. I was trying to prove that the probabilistic space of the correct laws of physics arising out of nothing by chance was infinite, since nothing cannot be measured. For example, the Lambda constant must be tuned to one part in 120 orders of magnitude. It's not that the odds of chance tuning it correctly are one in 120 orders of magnitude, rather the odds are infinite because there is nothing to restrict the probabilistic space. However, it would also follow that the amount of probabilistic resources are also infinite, since if nothing exists, then that would include probabilistic resources.

So what are the odds of scoring the right item out of an infinite list, if you have an infinite amount of time to try? I guess the odds would be 1. But I would also like to know what the odds of scoring the right item is, if the list is infinite.

This reminds of trying to figure out the probability of something occurring when the state space is uncountable, like in a continuous distribution like the Normal distribution.

When we deal with situations like this, you can't find the probability of "one" point since it is zero. Instead we find out the probability of an "interval", or in other words, the probability of falling in between some interval that has a length > 0.

 

[bobsmith76]

For example, the Lambda constant must be tuned to one part in 120 orders of magnitude. It's not that the odds of chance tuning it correctly are one in 120 orders of magnitude, rather the odds are infinite because there is nothing to restrict the probabilistic space.

Well you don't actually know that, do you?

If there is nothing, then there is really nothing.

If there is something that restricts probabilistic space, then that is not nothing, that is something.

 

[pmsrw3]

If there is nothing, then there is really nothing.

If there is something that restricts probabilistic space, then that is not nothing, that is something.

Very deep, Buddha. Yes, if there is nothing, then there is really nothing, and the universe is not here. Is that really what you believe to be the case?

There are several problems with this. One of them, of course, is what you mean by "nothing". Another one is your assumption of a particular default probability measure. You believe that "nothing can restrict probabilistic space", but in deducing that the probability of a particular lambda is zero, you are in fact making restrictive assumptions about its probability space. Another is that you (and I and everyone else) doesn't really know what lambda is. It is entirely possible that the underlying nature of the CC restricts its possible values. Also, in assuming that the probability of the CC having the value that is has is zero, you're assuming that lambda actually DOES have a particular value. It is entirely possible (and indeed, quantum mechanics would seem to demand this) that the CC is a very tiny bit fuzzy -- i.e., rather than being one number, it has a wavefunction spread out over a small range of possible values.

 

[bobsmith76]

If there is nothing, then there is really nothing.

If there is something that restricts probabilistic space, then that is not nothing, that is something.

Very deep, Buddha. Yes, if there is nothing, then there is really nothing, and the universe is not here. Is that really what you believe to be the case?

This is the fallacy of equivocation. There are at least two types of nothing, one, the nothing that existed before the first event, and two, nothing that exists in our everyday world. These are two completely different things. What you're saying is:

1. nothing exists in our present reality
2. probability space is restricted
3. therefore, probability space could be restricted before the First Event when nothing existed

That's the fallacy of equivocation because nothing has two different meanings in 1 and 3.

There are several problems with this. One of them, of course, is what you mean by "nothing". Another one is your assumption of a particular default probability measure.
You believe that "nothing can restrict probabilistic space",

The opposite is true. Before the first event nothing existed, including restrictions on probability space.

but in deducing that the probability of a particular lambda is zero, you are in fact making restrictive assumptions about its probability space.

I never said that. I said: "For example, the Lambda constant must be tuned to one part in 120 orders of magnitude. It's not that the odds of chance tuning it correctly are one in 120 orders of magnitude, rather the odds are infinite because there is nothing to restrict the probabilistic space."

Another is that you (and I and everyone else) doesn't really know what lambda is.

I didn't know this, but I have no pretensions to being an expert on physics. Thank you for pointing that out.

 

[pmsrw3]

This is the fallacy of equivocation. There are at least two types of nothing, one, the nothing that existed before the first event, and two, nothing that exists in our everyday world.

There are many types of nothing, but, contrary to your understanding, I was only referring to one, the same all-encompassing one you described, in which "If there is nothing, then there is really nothing." If nothing existed "before the first event", then it would be impossible for anything to exist now. For nothing, if it is really nothing, does not include the potential for a future.

but in deducing that the probability of a particular lambda is zero, you are in fact making restrictive assumptions about its probability space.

I never said that. I said: "For example, the Lambda constant must be tuned to one part in 120 orders of magnitude. It's not that the odds of chance tuning it correctly are one in 120 orders of magnitude, rather the odds are infinite because there is nothing to restrict the probabilistic space."

You didn't say it, but what you did say, in your own statements that you just quoted, imply it. You can't deduce that the probability of a particular lambda is 0 without making assumptions about the probability measure. You call these assumptions "nothing to restrict the probability space", but since they are true of some probability spaces and false of others, they do in fact restrict the probability space. This is why the measure problem is such a puzzle. You can't make any statements about the probability of a particular universe without making some assumptions about the probability space from which they spring, and any such assumptions constrain the possible probability spaces.

 

[bobsmith76]

You didn't say it, but what you did say, in your own statements that you just quoted, imply it.

When I said that the odds are infinite, I meant that they cannot be measured and that there literally isn't a probability space.

You can't deduce that the probability of a particular lambda is 0 without making assumptions about the probability measure.

I don't believe it can be deduced.

You call these assumptions "nothing to restrict the probability space", but since they are true of some probability spaces and false of others, they do in fact restrict the probability space.

If we're talking about a universe coming into being literally from nothing, and when I say nothing I mean nothing, not the nothing that Lawrence Krauss talks about, then there is literally nothing that can restrict any of the natural laws falling between certain values, that is, if you're an atheist. The CC could have fallen anywhere on an infinite range. Some atheists try to get around the enormous odds of all the various physical laws being tuned with knowledge of each other and say that natural law tuned the laws, not chance. But then you just ask where the natural laws came from. There are only two possibilities: chance or not chance. If you're an atheist you must believe that it is chance that produced the natural laws. Chance can't tune natural laws purposefully.

You can't make any statements about the probability of a particular universe without making some assumptions about the probability space from which they spring, and any such assumptions constrain the possible probability spaces.

I agree.

 

[pmsrw3]

When I said that the odds are infinite, I meant that they cannot be measured and that there literally isn't a probability space.

I see. Perhaps you will understand why that confused me. To me that "the odds are infinite" is a specific mathematical statement. The statement "There isn't a probability space" is literally inconsistent with the statement "The odds are infinite". It's like saying, "Beauty cannot be measured" and "Her beauty is 50 milliHelen." It's hard for me to understand how anyone could write "the odds are infinite" and expect it to be interpreted as "the odds ... cannot be measured and ... there literally isn't a probability space".

If we're talking about a universe coming into being literally from nothing, and when I say nothing I mean nothing, not the nothing that Lawrence Krauss talks about, then there is literally nothing that can restrict any of the natural laws falling between certain values, that is, if you're an atheist. The CC could have fallen anywhere on an infinite range.

You say that there is nothing that can restrict any of the natural laws, but then you immediately state that this implies a restriction. That final statement (in bold) is not "nothing". It's a very definite statement that has definite restrictive implications for the nature of the universe and the laws of physics. The statement "nothing that can restrict any of the natural laws falling between certain values" is likewise a restriction. True, it is a restriction of a different type than the naive idea of fixed bounds, but it very clearly excludes certain possibilities, and is therefore a restriction. Neither of these can come from the nothing nothing you're insisting on -- they are specific statements about the probability space from which the CC emerged. If there was really nothing, in the sense you insist on, there was nothing on which such deductions would be based.

 

[bobsmith76]

I see. Perhaps you will understand why that confused me. To me that "the odds are infinite" is a specific mathematical statement. The statement "There isn't a probability space" is literally inconsistent with the statement "The odds are infinite".

It's like saying, "Beauty cannot be measured" and "Her beauty is 50 milliHelen."
[/quote
If I say beauty is 50 millihelen, then that is not infinite.

It's hard for me to understand how anyone could write "the odds are infinite" and expect it to be interpreted as "the odds ... cannot be measured and ... there literally isn't a probability space".
[/quote
The very definition of infinite is that which cannot be measured.

You say that there is nothing that can restrict any of the natural laws, but then you immediately state that this implies a restriction.

No I didn't.

That final statement (in bold) is not "nothing". It's a very definite statement that has definite restrictive implications for the nature of the universe and the laws of physics. The statement "nothing that can restrict any of the natural laws falling between certain values" is likewise a restriction. True, it is a restriction of a different type than the naive idea of fixed bounds, but it very clearly excludes certain possibilities, and is therefore a restriction. Neither of these can come from the nothing nothing you're insisting on -- they are specific statements about the probability space from which the CC emerged. If there was really nothing, in the sense you insist on, there was nothing on which such deductions would be based.

You're not understanding me. First, there is nothing. In that nothing you can't put a probabilistic space on it because there is literally nothing there. When something comes out of that nothing, it could literally be anything. I'm not saying that only an X between A and Z can come out of nothing, I'm saying that literally anything can come out of nothing, no restrictions. The CC can come out nothing and before it arose it was unrestricted, but after it completed its coming into existence it operated within a bounds, maybe.

I'm not going to participate in this discussion any more because it seems that we're in agreement, but you're having trouble understanding what I'm saying. The discussion has descended into a useless quibble about some very minor technical issue.