For the past fifteen years, the anti-evolutionist literature has been dominated by mathematical arguments, typically drawn from the fields of probability theory, information theory, and combinatorial search…. But when the arguments are shorn of their technical pretensions and presented in readily comprehensible language, it is never difficult to spot the fatal conceptual flaws at their core.
A classic anti-evolutionist argument now goes like this: A gene can be viewed as a sequence of letters, just as the outcomes of multiple coin tosses can be viewed as a sequence of Hs and Ts. If a specific gene is, say, 100 bases long, then the probability of getting just that sequence by random chance is 1/4 multiplied by itself 100 times. This is such a small number, the argument continues, that it could not possibly have been the outcome of a naturalistic process and must instead have arisen through intelligent design.
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However, this argument is premised on the notion that genes and proteins evolve through a process analogous to tossing a coin multiple times. This is untrue because there is nothing analogous to natural selection when you are tossing coins. Natural selection is a non-random process, and this fundamentally affects the probability of evolving a particular gene.