There is more atheists than...

Originally posted by googlefudge
By mandatory I meant probability 1-e Where e=1/infinity...

Which is 1 for all practical purposes.

Well I think that is very bad use of the word 'mandatory'.
Take my earlier example: given an arbitrary real number the probability that it is not an integer is 1-e Where e=1/infinity...

Is it mandatory that the number will not be an integer? According to you, yes, but it doesn't fit well with the meaning of the word in the dictionary.

Originally posted by googlefudge
However lets for the moment stick with the most basic, a 3 dimensional universe
that stretches infinitely in every spacial dimension, (and for the moment we'll
specify that it extends infinitely into the time dimension as well.)

Could an infinitely large black hole exist in your hypothetical universe? Does that mean that it does exist?
Could an infinite area of uniformly spaced hydrogen atoms that fills your whole universe exist in your universe? Does that mean it does exist in your universe?

Originally posted by twhitehead
Well I think that is very bad use of the word 'mandatory'.
Take my earlier example: given an arbitrary real number the probability that it is not an integer is 1-e Where e=1/infinity...

Is it mandatory that the number will not be an integer? According to you, yes, but it doesn't fit well with the meaning of the word in the dictionary.

woha... apart from not being a reliable analogy...

the probability of an arbitrary real number isn't 1-(1/infinity)

it's cardinal 1 infinity over cardinal 2 infinity.

There being an infinite number of integers.




For an event to be possible in this universe it must have a probability of occurring > 0

For any event with a probability of occurring > 0 in an infinite universe their will be an
infinite number of occurrences.

The only question being how far apart these occurrences are.

Originally posted by twhitehead
Could an infinitely large black hole exist in your hypothetical universe? Does that mean that it does exist?
Could an infinite area of uniformly spaced hydrogen atoms that fills your whole universe exist in your universe? Does that mean it does exist in your universe?

Assuming such things are possible within the laws of physics then yes.

You can fit infinitely large objects inside infinitely large space with an infinite amount of space left over.

Originally posted by googlefudge
You can fit infinitely large objects inside infinitely large space with an infinite amount of space left over.

Can you make a shoe rack for my wife?

Originally posted by googlefudge
Assuming such things are possible within the laws of physics then yes.

You can fit infinitely large objects inside infinitely large space with an infinite amount of space left over.

I think you missed the second one. My infinitely large area fills all of your infinitely large space. It is physically possible.

Originally posted by googlefudge
the probability of an arbitrary real number isn't 1-(1/infinity)
it's cardinal 1 infinity over cardinal 2 infinity.
There being an infinite number of integers.

But the real numbers can be thought of as an infinite set of integer intervals each including the smaller integer but not the larger. An arbitrary integer will fall into one of those intervals and its probability of not being the integer is 1-(1/infinity).
Sorry, but I have a degree in maths and still remember a few things here and there.

For an event to be possible in this universe it must have a probability of occurring > 0
I disagree. Give an argument as to why it must have such a non-zero probability of occurring.

Suppose a finite universe were empty of matter. Would an atom in such a universe be said to be impossible? If so, then your definition of 'possible' simply means 'it exists' and your whole claim is a tautology.

Originally posted by twhitehead
I think you missed the second one. My infinitely large area fills all of your infinitely large space. It is physically possible.

Actually I am not sure that it is.

In infinitely large area of evenly spaced hydrogen atoms filling all of space would collapse
because of the uncertainty principle making their positions indefinite and the fact that they
will start decaying radioactively.

So I don't think that falls into the category of things that are physically possible.

Originally posted by twhitehead
But the real numbers can be thought of as an infinite set of integer intervals each including the smaller integer but not the larger. An arbitrary integer will fall into one of those intervals and its probability of not being the integer is 1-(1/infinity).
Sorry, but I have a degree in maths and still remember a few things here and there.

[b]For an ev ...[text shortened]... then your definition of 'possible' simply means 'it exists' and your whole claim is a tautology.

I hate infinities.

I think the problem here is that you are looking at this like a mathematician
and I am looking at it as a physicist.

In you're finite universe that is "empty of matter" you will have matter popping in and out of
existence all the time as virtual particles.

Physics has constraints on it that mathematics doesn't.

Basically if you have a large enough space and wait long enough anything possible to occur
will occur.

Originally posted by wolfgang59
Can you make a shoe rack for my wife?

Is her shoe collection countably or uncountably infinite?

Originally posted by twhitehead
I think you missed the second one. My infinitely large area fills all of your infinitely large space. It is physically possible.

My hypersphere can beat up your cube any day of the week, plus Sundays. You can take that to the bank!

Originally posted by twhitehead

[b]For an event to be possible in this universe it must have a probability of occurring > 0
I disagree. Give an argument as to why it must have such a non-zero probability of occurring.

Suppose a finite universe were empty of matter. Would an atom in such a universe be said to be impossible? If so, then your definition of 'possible' simply means 'it exists' and your whole claim is a tautology.[/b]

I don't think there is such an argument.

Let S represent the sample space of an experiment, which is the set of all possible outcomes the experiment may yield. An event E is a subset of S. The elements of E are said to be the outcomes of the experiment that are "favorable" to the event in question occurring. If the experiment consists of rolling a six-sided die, then S={1,2,3,4,5,6}. An event E might be the event of rolling an even number, so E={2,4,6}.

Let n(S) denote the number of elements in S, and n(E) the number of elements in E. In the case when S is a finite set, the probability of event E occurring is:

P(E) = n(E)/n(S).

If S={1,2,3,4,5,6} and E={2,4,6}, then the probability of rolling an even number with a six-sided die is P(E) = 3/6 = 0.5. Well, that figures!

In the case when S is infinite (whether countably or uncountably infinite), this just breaks down. If, hypothetically, all the counting numbers (1,2,3,&hellip😉 were put into a hat, the probability of drawing the number 9 would have to be said to be zero, based on the definition of probability given above (1 divided by infinity). And yet, a 9 could be drawn!

That's just the way it is. It's one of the reasons I quit studying statistics years ago and switched to pure mathematics.

In any case, if the universe -- if all universes in a hypothetical multiverse -- are quantized at the smallest scale, then it's fair to say that every physical inquiry is ultimately at most countably infinite (the infinity of the integers). The uncountable infinity of the real numbers (the continuum) is merely a convenient approximation.

Originally posted by googlefudge
I think the problem here is that you are looking at this like a mathematician
and I am looking at it as a physicist.

In you're finite universe that is "empty of matter" you will have matter popping in and out of
existence all the time as virtual particles.

Physics has constraints on it that mathematics doesn't.

Basically if you have a large enough space and wait long enough anything possible to occur
will occur.

So you are taking into account results of quantum mechanics -specifically the fact that space is constantly changing at random. Now that does affect the probability calculation and I'll have to agree with you - on the condition that quantum mechanics is right on that score - I am not convinced that it is.

Essentially random input over an infinite time does result in full coverage of the solution space. However input that is not known to be random, is not guaranteed to cover the solution space. So, for example if it turns out that quantum mechanics does not allow objects larger than a bus popping into existence, it might turn out that certain objects could not occur in your universe even if they were physically possible.

Further, you may be violating some physics by postulating infinite space and time.

Originally posted by googlefudge

For an event to be possible in this universe it must have a probability of occurring > 0

Despite what I said in my previous post, I think you may be right. In other words, you and twhitehead are both right in some sense. You're physically right and he's mathematically right.

Ignoring for the moment the possibility that the universe may have an infinite lifespan (expanding forever and ever&hellip😉, I think perhaps there are only a finite number of possible events that can occur in this universe in any finite time span, even when you factor in virtual particles popping in and out of existence. The real infinity comes in when you consider that other universes besides our own are also popping in and out of existence, and will do so forever. There is the multiverse, and then there are the parallel universes of the "many worlds" hypothesis in quantum theory. Thus, all things that are possible must occur. That is the "many worlds" interpretation.

Originally posted by twhitehead
So, for example if it turns out that quantum mechanics does not allow objects larger than a bus popping into existence, it might turn out that certain objects could not occur in your universe even if they were physically possible.

I think the only limit is the size of the universe.

Let's just assume the universe is a fixed size for a moment, with a finite lifespan. Space and time are quantized, or so the theory goes, and so there are only a finite number of "space-time slots" that can be filled in during the life of the universe. Each of those slots can only be occupied by a finite number of different kinds of particles. Each of those particles can only assume some finite number of different possible energy states, and can have only a finite number of different possible momentum vectors. And so on. Even if quantum mechanics dictates that the way the slots are filled is random, random does not mean infinite. In a quantized universe with a finite lifetime, therefore, there are only a finite number of possible events.

Now let the universe expand, so that space slots are being created over time. Even then, if the lifetime of the universe is limited, then my previous argument still holds, because only a finite number of additional space slots can be generated before the show is over.

If you let the number of time slots be infinite, then my argument fails. But, like you, I don't take that as a given.