So what? See post #6.
Kimstu Yes I understand something will happen, but the law of big numbers will tend towards a certain outcome, so those cards will tend to approach a equal distribution as the number of trials increase towards infinity.
Pochacco your posting severus’ post has the problem of the law of large numbers again if you take the monkey as a random typer.
It’s a thought experiment. As I pointed out above I don’t expect it to prove the existance of God, as God will not allow that.
I’m not sure what you mean by this.
Basically, what he’s saying is: In an infinite sample space, an event can have probability zero and yet still occur.
Why not?
In other words, if you deal out bridge hands at random for an infinite number of times, all possible hands will appear equally often (i.e., infinitely many times). Right.
But what does that have to do with the question of the universe and the existence of life? The universe is not infinitely old (not according to all currently accepted cosmological theories, anyway), so no analogy involving an infinite number of trials is applicable to events in the universe.
I think **Kimstu ** has it just right. We have only one universe where things happened the way we are seeing them happen. The probability of this particular universe happening is zero (well, not really but close enough), yet it happened. Had any other universe come to happen, we would be here sitting on our purple mushrooms poking at clay telepathomatics with our noses debating why we don’t sit on chairs typing on computers.
I think the point that **kanicbird ** was trying to make is that if something is impossible in an infinite number of trials, then it must be impossible in a finite number of trials as well.
However, he has failed to establish that either life or creation is impossible in an infinite number of trials.
But isn’t that wrong? For example, if we flip an infinite number of fair coins, it’s impossible that they all come up heads. Yet if we flip any finite number of fair coins, there is a calculable finite non-zero probability that they all come up heads. Ergo, impossible in the infinite case, possible in the finite case (though still very improbable if the finite number is large).
Both the premises in the OP are true (or, at least, the probability that they are not true is infinitesimal), and they are not contradictory. Yes, in an infinite number of tries there will be an infinite number of heads. On an infinite number of tries there will also be an infinite number of tails. On an infinite number of tries there will be an infinite number where the distribution is 50-50. On an infinite number of tries there will be an infinite number where the distribution of throws is 90-10 in favour of heads. It all depends on which infinite subset of that infinite set of throws you look at.
Note that none of the above says that the proportion of heads (assuming a fair coin) will approach 50% closer and closer as the number of throws gets larger and larger (i.e. as the number of throws tends to infinity).
There’s lots of interesting paradoxes when you start trying to play with infinities themselves rather than finite quantities that grow without bound, e.g. there are just as many integers as there are integers that are divisible by 2, just as many integers as rational numbers (x/y where x and y are integers), etc. etc.
Infinity is a funny thing. For example, did you know that there are as many even whole numbers as there are whole numbers? Or that there are fewer whole numbers than numbers between 0 and .000000000000000000001?
Ah, but I think you’re comparing apples and oranges. There are two different events here – in the first case you’re looking for an INFINITE number of coins to turn up heads, and in the second you’re looking for a FINITE number of coins to turn up heads. Not the same event at all. The phrasing “all the coins” hides the fact that we’re talking about two different sets.
You’ll note that in his original formalation of the problem **kanicbird ** was careful to compare one coin flipped an infinite number of times with an infinite number of coins flipped an infinite number of times to avoid this problem.
Umm, I’m not that well versed in probability, but I’m pretty sure there is no way you can prove that. The universe, life, “creation” – all obviously did happen. I’m not sure if that makes them dead certainties, but I’m quite positive that they cannot be impossible. Else how could we be here talking about it?
Kind of a hijack and possibly doesn’t need saying anyway, but I’ve seen these arguments many times and in my experience, they always make ridiculous assumptions, such as:
-Trying to calculate the probability of an entire cell forming spontaneously and entirely out of random chemicals (which of course bears absolutely no resemblance to anything any proper scientist might say about the possible origins of life0
-Ignoring chemical affinities - i.e. assigning every atom in the thought experiment an equal probability of bonding with every other atom, regardless of the element
-Pretending the universe would only have the opportinuty to take one shot at a time at creating life in one specific location (i.e. ignoring scaling)
And that’s in addition to any simple errors of mathematics, assumed values of variables, etc.
Unfortunately claiming that the two can’t coexist is a result of using the logic that’s true for numbers on infinity which is not a number. You simply can’t do mathematical operations with infinity and the logic of mathematics doesn’t apply to infinity.
a + n cannot equal a.
∞ + n equals ∞
The second statement isn’t a mathematical statement even though it is in mathematical form. All is says is that the result from adding any finite number to an endless quantity is still endless.
You are essentially saying that what we cannot currently (or perhaps ever) explain leaves only God(s) as a possible explanation. I’m pretty sure that’s how the whole concept of religion began in the first place. We are well on our way to explaining 99% of what was a mystery 25,000 years ago. I wouldn’t hang my hat on the last fractional percent of what is unexplained.
In any case, I do agree that God did not “design the system for Him to be proven” unless he wants it proved that there is an uninvolved Malicious Designer for what is obviously a broken and troubled dog-eat-dog creation full of random and hurtful capricious events.
Back to watching chimps slaughter one another and baboons eat flamingos alive on the Nature channel…the news from Iraq and Darfur is just too depressing.
It’s perfectly well possible to flip an infinite number of fair coins and have them all come up heads. The probability of this is 0, but a probability of 0 is not the same thing as being impossible (as remarked upon above by Pochacco and his quoting of severus).
In fact, no matter what particular exact outcome you get after you flip an infinite number of fair coins (e.g., first coin tails, next three heads, next two tails, …), its a priori probability was 0. Which should really put the nail into the coffin of the idea that a probability of 0 is the same thing as impossibility.
As to the Law of Large Numbers which keeps getting invoked, all its various formulations are actually only of the form “… happens with probability 1”, rather than “… happens for sure”. Just as a probability of 0 isn’t the same thing as impossibility, a probability of 1 isn’t the same thing as completely guaranteed.
Okay, I see, thanks.
And the probability of getting a particular configuration in any finite number of tries is not zero, so it’s even more obviously not impossible.