We can calculate the odds of data being already sequenced on a hard drive when it is formed. We can know the mathematical probability of characters that are formed by pebbles falling on keyboards - making an English word. Likewise, we can derive the probability / improbability of bases sequencing themselves without intelligent intervention into DNA strands capable of creating life. And the odds for such occurances aren't good. The author shows that for our alphabet, non-intelligent key-presses are unlikely to ever form sentences of more than 96 characters, with "ever" being defined as 17 Billion years for 17 Billion Earth-like planets. That is a mathematical way of saying that large, long, complex sequences do not form naturally.I wouldn't argue with the mathematical results you propose--in a mathematical universe. A mathematical universe has no characteristics within it that were not put into it. For instance, a mathematical keyboard would never have to face the misfortune of keys being jammed after being bombarded for a very, very long time by little pebbles.
In a real universe the keyboard would have to deal with the forces of nature: gravity, the strong force, the weak force and electromagnetism. In a pristine mathematical universe hydrogen could bounce around forever and remain nothing but hydrogen. But in a universe with the natural cosmic forces at play, you start with hydrogen and get--at minimum--the known periodic table...and that's before even thinking about the unknown properties of the universe, like dark matter.
But don't the physicists say that the "real" world IS the mathematical world? What is the difference between the two?