Mathematically, the billions of years still amounts to small numbers. When the probability of an event is a fraction, and you calculation the probability of millions of events in sequence, those fractions become impossibly small. One example is the (im)probability of all of the proteins in the human.body arising by chance - you start to get a figure as likely as choosing the correct atom out of our solar ssystem by chance. Similarly, the force required for the big bang is so finely calibrated that the probability of it being randomly correct is like picking one nanosecond correctly out of the entire period of the universe's existence. The other old analogy is that a billion monkeys typing randomly for a billion years would never land up typing a Shakespeariam play.

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