One of the mathematical implications of random walks or Brownian motion is that after enough random outcomes, the universe of possible future outcomes is smaller than the universe of possible future outcomes was at time t=0.
Model enough random walks and you will see different walks yield mutually exclusive future outcome universes.
How are we to conclude that truly random mutations will by mathematical necessity produce homo sapiens?
That's even without taking into account the archeaological record of numerous mass extinctions, often precipitated by catastrophic natural disasters, which can drastically alter the universe of future outcomes in a short span of time and is completely external of the process of natural selection.
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