A good buddy of mine and I have had a friendly debate about the origins of the current state of our universe (namely; Earth and life on Earth) and have fundamentally disagreed in our stances with respect to probabability, infinity in time and space and possible/probable event outcomes. He maintains the position that given a set of possibilities and enough trials, each outcome must have occured; which is his reasoning for why life must exist. I do not necessarily take issue with this particular concept, as given an infinite amount of time and states of matter life is bound to come from one of those states. In our discussions, however, we have been using a specific example in which I disagree vehemently with his stance. The example:
If you throw a handfull of sand in the air an infinite number of
times, and that sand lands on a flat surface, every
configuration will happen (according to his position). For instance,
the sand landing in a pattern which spells your name out is a
mathematically possible outcome, and will therefore happen given
enough trials.
To counter his stance on this example, I took the position that there is a mathematical (but not physical) possibility that every grain of sand lands in the same one inch square of the surface; but I maintain that even though it is a mathematically possible outcome it will never happen because of the way the physical world works – that sand will be roughly evenly distributed for each throw, even if over an infinite number of trials, assuming consistent and fair trials (ie, no God or other being moving grains of sand). I submit that even though it is a mathematical possibility, you'll never see your name spelled out in block letter English anywhere in the universe without the influence of intelligence, even if you were able to attempt a verification for this – he disagrees. I held him liable for mathematical/physical proof of reasoning for his stance and he has taken to dismissing me as ignorant of probability and infinity. Can anyone provide some good reasoning for either side of this argument? I realize that either is an impossible stance to prove, since we can't verify our positions, but any well-reasoned insight will be appreciated. A similar question, with an answer I found to be relatively useful:
Infinite universe – Jumping to pointless conclusions
EDIT:
After reading some of the comments and answers here it has become apparent that I may have misrepresented my ultimate question. I realize that given a non-zero probability and an infinite number of trials, the mathematical probability of encountering the event described by said probability converges to 1. Some have taken the position that there is no disconnect between a mathematical probability and the likelihood (read: possibility) of a physical event happening.
To simplify the argument, the surface can be thought of as a grid – in which case every single configuration has some mathematical probability associated with it. My stance regards certain configurations as physically impossible, however, which is the reasoning behind my one-inch-square analogy. Can anyone show clear reasoning (and sources!) for their belief that it is possible to toss a handful of sand into a one inch square?
Best Answer
Physics uses mathematics. In a thought experiment of a machine ( to exclude the complications of hand throws that John mentions), using statistical mechanics any configuration is possible so even the telephone catalog on the floor with names and addresses. Note "thought experiment" .
Physics calculates the probability of this happening in very strict mathematical formulas and puts physical limits on what is probable to be seen using statistical measures, standard deviations, to gauge the confidence we can have on any measurement/observation in physics . We accepted that we saw the Higgs because the combined experiments gave five standard deviations for it not to be a fluke/coincidence. One chance in 100.000 . Experiments with such levels of confidence have not been falsified in elementary particle physics experiments ( from repeated statistically experiments, discovering errors is another story).
The probability of getting a name from the above thought experiment is effectively zero, for physics, if one puts down the number of permutations in space .
Thus the answer to your controversy is: you are both in a sense correct. Your friend is looking at the thought experiment, and you are looking whether it can be physically realized, and physics does put a limit to probabilities, experimentally, with what we know and have measured as probable in nature.