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You do not need a book...

You do not need a book, but just one phrase, to show that species did not “form” or “evolve” through random mutations: “the probability that a monkey pounding on a keyboard with 100 keys will come up with this phrase” exactly as written (with spaces, but without counting the quotes and without uppercase characters requiring key combinations), can be calculated as follows: The probability for the monkey (or a random process) to hit the first Character, a “t” on a keyboard is 1 out of 100 (101 key keyboards are the most common – let’s imagine one key being disabled). The probability for the first two characters (“th”) to be hit, in the proper sequence, is 1 out of 100 x 100, or 1 out of 1002  (or 104). The probability for all the 96 characters in the above phrase to be hit, in the proper sequence, is 1 out of 10096 (or 10192). This number is bigger that the number of all the vibrations all the atoms in the universe ever had. No “crude” random process (i.e.: not a computer program written by an intelligent programmer), even trying a million times per second, could have come up with the phrase above since the beginning of time. The number of seconds in an hour is 3600, in a day is 86,400, in a year is 31,536,000. This is (rounded up) 3.2 x 107 (seconds in a year). By multiplying this number by one million, we find that there are almost 3.2 x 1013 Microseconds (millionths of a second) in a year. Thus 100 Billion years (a mere 1011 years - five times what astronomers think the age of the universe is) is less than 3.2 x 1024 Microseconds, a number infinitesimally small, almost insignificant, compared to the number of random trials – one per Microsecond - required to compose our phrase: 10192. The above calculations give us an idea of the numbers involved in a random process of “generation”.  In the real world of DNA sequences and chromosomes, we need to consider some differences. We know that the DNA sequence, combination of chromosomes, genes and imbedded rules of one sexually reproducing animal species is much more complicated (or “longer”) than our phrase. On the other side, we know that many genetic sequences are “viable” (For specifics see NOTE 1 below). The idea of random mutations between one individual and its progeny has an innate problem: By definition, a random mutation can apply to any spot on the DNA sequence, of any chromosome of the parent individual and could simultaneously apply to some, or a large part, or most of the genetic information. Assuming otherwise, would require some other intervening process. For example, could an ape develop one more toe to be able to grab things better? If we entertain other concepts, such as adaptation to the environment, or some other theory, working in conjunction with random mutations, then random mutations need to be severely limited, or any progeny would have a very large probability of not being viable. The more we limit the concept of random mutations, the more time is needed to produce their intended effect (a genetically different viable individual). But we have seen, from our calculations, that random variations do not have enough time to work their magic even if they happened a million times per second. Any severe restriction imposed on them by some other reasoning, for example by introducing a process of adaptation involving several generations of individuals of that species, would further invalidate the theory of random mutations. Thus, considering random mutations independently from other processes, the probability for a particular random genetic mutation to generate a progeny able to survive or thrive is equivalent to the probability of producing a workable DNA sequence for all of its chromosomes randomly from scratch. As we read in the “random mutation” literature, a mutation is “unrelated to how useful that mutation would be”. Mutations, in conformance with the theory, include the possibility of producing a different species altogether! Thus, according to our calculations, not even one viable animal species  could have been randomly “defined” or “re-defined”, trying new combinations a million times a second, during the time the universe has existed, rounded up to 100 Billion years (or a trillion times that, if you want). We are very generous with the age of the universe on purpose, even if the “Cambrian explosion” is estimated to have happened less than 1 Billion years ago. Furthermore, how would the random process know, without an “external intelligence” which combination is the right one, once it is achieved? If interested, see NOTE 2 below. In conclusion, a random mutation scenario for the generation or transformation of animal species is so far from the realm of mathematical possibility to make it ridiculous to entertain, even as part of, or in combination to other possible processes or theories.   NOTE 1: The DNA sequence of a sexually reproducing animal may be between 50 to 250 million characters long: This is a repeated sequence of combinations out of only four letters (Amino-acids A,C,G,T), equivalent to a “keyboard” with only 24 “keys” - one particular sequence out of the 24 possible permutations. We discard here the possibility of repetitions, which in some cases would increase the number of “keys”. We are also very approximate in our genetic analysis, because, as you will see, we have lots of “length” to spare. Our “phrase” is the length of the DNA sequence divided by 4 (each specific amino-acid group), that is between 12 and 60 million characters. Let’s just say it’s over a million characters long. This number needs to be multiplied by the number of chromosomes of that species (let’s forget about this, as this number is so small in comparison), and then divided by the number of viable DNA sequences. Let’s be generous and assume, for this calculation, that half of the DNA sequences would be viable. With this amount of viable mutations we would observe that half of the surviving progenies of any animal would display genetic mutations and/or would become completely new species! This is far from reality, I know, but let’s be very generous. Thus the number of “random trials” to define a viable DNA sequence for this animal would have to be at least 24 to the power of more than half a million (24500,000+)! By now you should have a “sense” that this approximate number is incomparably bigger (more than half a million orders of magnitude) than 10192, the number we used in our calculations above as the required number of random trials to generate our phrase!   NOTE 2: The theory of random mutation implies a “meeting” between two individuals of the same sexually reproducing species (Let’s forget about the low probability of two individuals of the same species being randomly generated in the same reproductive lifetime span – out of 100 Billion years. Let’s also forget about the low probability of them meeting in the same spot). They need time to growth to maturity, time for courting and reproduction, time for testing their survival, dying, etc. These are all processes that require much more time than a millionth of a second (which we assumed in our calculation as the time between random trials).  If it did take only 1,000 seconds (that’s about 17 minutes) for all of these processes to occur, then the amount of time required for generating a new species would increase by 9 orders of magnitude! However, we can forget this too, since we have more than half a million orders of magnitude to spare.