Quote:
Originally posted by Kyo
- The problem lies in this: assume you toss tails 30 times. "Well," you say to yourself, "the possibility of me tossing tails again is so low it might as well be zero, so my next toss will be a heads." And you toss ... and lo and behold, it's a tails!. You scratch your head in puzzlement and say, "Okay, well, now the possibility of tossing heads is even closer to zero, so my next toss must be a heads." And you toss again - and yet again, you get a tails! And again, and again, and again. Therefore, you cannot say that probability close to zero might as well be zero, so long as you are dealing with independant events.
- The coins relate to my argument in this fashion: unless you believe in chaos theory, I argue that events in the universe are, more or less, like tosses of that coin. Or rather, let us consider an infinite-sided dice, and consider some kind of celestial being (for the sake of example), which tosses this remarkable dice to determine the events of the universe. I argue that it is entirely possible to never roll the same number twice.
- To clarify - though you claim (and most agree) that the universe is infinite, I claim that there are an infinite number of possible events or sequences of events. When comparing infinite trials against an infinite number of possibilities, we are no longer able to assert that all possibilities will eventually come about - just as we could not assert that given infinite time we could toss all possible heads/tails sequences of a fair coin.
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As far as the coin, I do not disagree with what you said, but never did I say that the probability of getting heads or tails for one trial is close to zero. I said the probability of getting 30 tails in a row is so close to zero it might as well be zero.
In a row being the key words. This says nothing about the nth of 30 tosses, only that in 30 tosses you will almost surely toss both heads and tails.
Now then, if you have an infinite-sided die, I agree with you that it is possible to never roll the same side twice. Actually it is
impossible to roll the same side twice, by definition. You roll once say, on your second roll, there is one side you can roll to have a repeated side come up, but there are infinitely many that you haven't rolled, as such it is not possible for you to roll a repeat, because any constant over infinity is zero.
If the universe is infinite, or even large enough that you might as well call it infinite, that does not mean that there are an infinite number of possible events or sequences of events as you put it. First of all there are a finite number of elements, and that suggests to me that there would be a finite number of possibilities. Just think of it this way:
Think of the graph of 1/x. It is asymtotic to the x and y axis. Now, imagine that the graph is rotated about the x axis, to make the shape of a bell, as in the "bell of a trumpet or trombone. Or a curved funnel if you will. This is a three dimensional construct, and its surface area is infinite. However its volume is finite. How do we explain this apparant paradox? Well just imagine it this way. You will never get enough paint to cover the outside of the shape, but if you pour paint enough paint into it you will fill it. This is because the atoms that make up paint are some size, and as the bell gets closer to the x axis, they simply wont fit inside any further at some point.