Fine-tuning and infinity: a question

[Naraoia]

And probably a silly one.

I got the idea from The Elegant Universe, which I've just started. Somewhere in the first chapter, it says that the universe wouldn't be the same if the ratios of the strengths of fundamental forces would be only slightly different. Now, that's a (to me) new way of looking at the fine-tuning problem, since all I've ever heard about fine-tuning was concerned with the values of whatever constants.

(In retrospect, I should've realised that it's not the numerical values but the mathematical relationships that are important, but whatever...)

So... basically, there are infinitely many combinations of fundamental constants that produce exactly our universe; the numbers don't matter so long as they relate to one another in the correct ways. Since (AFAIK) the values of these constants are real numbers, the set of combinations that yield our universe is uncountably infinite.

Now, the set of all possible combinations of constants is also uncountably infinite. I'm not sure if they are the same size (all I know about the cardinality of infinite sets is Cantor's diagonal argument), but if they are, wouldn't that mean that "fine-tuning" doesn't exist? If the set of universes like ours is as big as the set of all possible universes, it's not that improbable that a universe like ours exists even if there's no multiverse...

Am I completely off the mark here? How does probability even work for universes?

Thoughts? Do be gentle

 

[Thistlethorn]

The fine-tuning argument always seemed like a huge pile of dung to me as the chance of something having happened after it did happen is 1. Imagine a deck of cards. Draw five cards. The chance of you getting the five cards you got before you drew them is astronomical. The chance of you getting the five cards you got after you drew them is 1. This applies to every hand. You simply cannot calculate probability after the fact.

All this is of course aside from the fact that the creationists using the fine-tuning argument fail on several other fundamental mathematical levels.

 

[AV1611VET]

I wonder just how effective the chance argument is anyway.

They say there were 109 of 333 prophecies fulfilled in Jesus' first advent; and the remaining 224 of 333 prophecies will be fulfilled in His second advent, an even harder task.

Yet how many will get saved based on that?

When the events of the Tribulation begin to unfold, and unfold in the order that they are documented in the book of Revelation, I wonder what effect that will have on persuading people to get saved?

Hopefully multitudes.

 

[[serious]]

The hole is fine tuned for the puddle in it.

Yes, life as we know it wouldn't exist if the universe were not as we know it. That isn't to say that life as we have not even imagined it would be impossible.

 

[Gracchus]

Some of the numbers just have to be what they are, which means some of the ratios also have to be what they are.

For instance, pi has to be what it is. Epsilon could not have any other value.

Some just things have to be what they are.

That is why I tell the Witnesses who come to my door that I get all my theology out of a mathematics book.

 

[Chesterton]

If the set of universes like ours...

Wait, wait...the what? Is this a faith thing?

 

[metherion]

Well, you see, if there are infinite number of possible combinations that produce universes like ours, there must also be an infinite number of those that do NOT. So, then if you wander into transinfinite math, your head explodes and the rest of us go on wondering.

After all, when the probability is infinity over infinity, what do you do? Lol.

Metherion

 

[Spashie]

An infinite number of universes?

Well, its a really great idea, i can tell you that. But as of now, there's no evidence of the multiverse hypothesis.

Personally, I tend to go towards the cyclic universe model.

 

[[serious]]

An infinite number of universes?

Well, its a really great idea, i can tell you that. But as of now, there's no evidence of the multiverse hypothesis.

Personally, I tend to go towards the cyclic universe model.

current measurements seem to indicate that we don't have enough mass to pull everything back in.

 

[cerad]

current measurements seem to indicate that we don't have enough mass to pull everything back in.

Unless dark energy reverses itself.
On the trail of dark energy - CERN Courier

Some even lead to an eventual reversal of the acceleration and a collapse of the universe. It is amusing that the first dark-energy model, the linear potential, possesses this quality.

 

[LordTimothytheWise]

And probably a silly one.

I got the idea from The Elegant Universe, which I've just started. Somewhere in the first chapter, it says that the universe wouldn't be the same if the ratios of the strengths of fundamental forces would be only slightly different. Now, that's a (to me) new way of looking at the fine-tuning problem, since all I've ever heard about fine-tuning was concerned with the values of whatever constants.

(In retrospect, I should've realised that it's not the numerical values but the mathematical relationships that are important, but whatever...)

So... basically, there are infinitely many combinations of fundamental constants that produce exactly our universe; the numbers don't matter so long as they relate to one another in the correct ways. Since (AFAIK) the values of these constants are real numbers, the set of combinations that yield our universe is uncountably infinite.

Now, the set of all possible combinations of constants is also uncountably infinite. I'm not sure if they are the same size (all I know about the cardinality of infinite sets is Cantor's diagonal argument), but if they are, wouldn't that mean that "fine-tuning" doesn't exist? If the set of universes like ours is as big as the set of all possible universes, it's not that improbable that a universe like ours exists even if there's no multiverse...

Am I completely off the mark here? How does probability even work for universes?

Thoughts? Do be gentle

I don't know. I don't think that if you are trying to get organized matter, for example, that you could adjust strong or weak nuclear force, and make up for them by tweaking other constants.

On the other hand, if that somehow did work, I don't know what that means... because you still have an extremely small margin of error.

Kind of like there are infinite stickers in 2 rows to make a simple analogy. Every quintillionth sticker in row 1 is blue, and every sticker in row 2 is blue. Do both rows have the same number of blue stickers?

 

[[serious]]

I don't know. I don't think that if you are trying to get organized matter, for example, that you could adjust strong or weak nuclear force, and make up for them by tweaking other constants.

On the other hand, if that somehow did work, I don't know what that means... because you still have an extremely small margin of error.

Kind of like there are infinite stickers in 2 rows to make a simple analogy. Every quintillionth sticker in row 1 is blue, and every sticker in row 2 is blue. Do both rows have the same number of blue stickers?

same number, lower density. Also, with a sample size of one, it means nothing to draw a blue sticker. Even more so if you are only capable of inspecting draws that return blue stickers.

 

[LordTimothytheWise]

same number, lower density. Also, with a sample size of one, it means nothing to draw a blue sticker. Even more so if you are only capable of inspecting draws that return blue stickers.

In terms of the analogy though, if you are aware that the chances of drawing a blue sticker are one in a quintillion, such a draw would still be surprising unless you are presupposing other draws existed.

 

[[serious]]

In terms of the analogy though, if you are aware that the chances of drawing a blue sticker are one in a quintillion, such a draw would still be surprising unless you are presupposing other draws existed.

if we were only capable of observing the draw if it turned out blue, there would be nothing odd about an observed draw being blue regardless of how many draws may have occured. Had life not developed there would be no life to inquire as to the chances of life occuring. As such, a specific answer is a precondition of the question. It may be that there were other draws, we don't know, nor does it matter. Trying to calculate the odds of something that already happened after it happens is a bit of a fools errand if the only objective difference between it and other possibilities is that that was the one that happened.

 

[LordTimothytheWise]

I think we are all aware of the anthropic principle, its criticisms and rejoinders, but that aside, what do you think of the infinite possible fine tuned worlds undermining fine-tuning arguments on the issue of probability? (presuming that part of the question for the sake of argument)