I don't think I did, but feel free to point out where you believe I did, and where my analysis is faulty:
Or are you one of those who insist that a room full of monkeys with keyboards can write the complete works of Shakespeare?
In theory? Yes they can, if you're willing to wait long enough (where "enough" is an amount of time that boggles the imagination). In practice (by simple random output)? No they can't.
But they can do it pretty quickly and easily if a replication and selection process is involved.
You wanted to see a calculation, so let's do one.
Consider the Shakespeare phrase, "If you can look into the seeds of time, and say which grain will grow and which will not, speak then unto me." That's 109 characters (including spaces and punctuation). Upper and lower case letters, plus digits and puntuaction, make up a pool of about 70 different characters. This means that the odds of producing the Shakespeare phrase in one random trial is 1 out of 70109, or 1 in 1,305,227,939,201,292,014,528,313,176,276,968,928,001, 249,110,077,400,839,115,038,451,821,150,802,274,449,576, 205,527,736,070,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000.
Needless to say, that's a big number. It's so huge that if every atom in the universe (about 1080 of them) were a computer capable of making a billion (1,000,000,000) random trials per second, the expected time required to produce the above line from Shakespeare would be 2,585,011,097,170,911,314,802,759,827,024,569,612,393, 783,728,161,759,843,736,212,615,624,189,581,658,716,078, 309,043,891,309 times the expected lifespan of the universe. That's close enough to "never" in my book.
But that's for *purely* random production process. How much do you think an evolutionary process could cut down that figure? Knock a few zeros off the end, maybe?
Well let's try it. Using an evolutionary process, which couples random variation with replication and selection and *nothing* else, the above Shakespeare phrase can be produced on a *single* computer (mine), using a breeding population of 1024 character strings in a whopping... 15 seconds (using this applet):
Generation: 0Hmm, 15 seconds is a hell of a lot faster than zillions of times the lifespan of the universe, isn't it? Evolution sped things up (compared to a purely random process) by a factor of more than 1045 (that's a "1" followed by forty-five zeros).
Tries <= 1024
Best Critter: "xSeOSEpc3Lm6rnRWnpFYL?QEDY7a67XlfRoJ0e8Len'X'1u'BhdrNqSNaXr7kVjondNozkf2CH9d96SaI?'f43M.CUGJ5XHbqfeR.UJP'tgNP"
Score (0 is best) 101Generation: 100
Tries <= 26624
Best Critter: "vf,ioV c3RKlooioifBFQXh, PeHTskof!oJ0e,Lrn'X'1u BhkchESNaXr kVjo dNozpanSI div1Qwi8h taQ,jswMkk,us1S'ugYtmm7."
Score (0 is best) 72[...]
Generation: 1115
Tries <= 286464
Best Critter: "If you can look into the seeds of time, and say which grain will grow and which will not, speak then unto me."
Score (0 is best) 0Checked 286464 critters in 15 seconds == 19097 tries/sec.
Lesson: Evolutionary processes are *incredibly* more efficient and effective than simple randomness alone.
Hmmm... just WHO decides the 'selection critria'? The Man behind the Curtain??
No. For biological evolution, survival itself provides the selection criteria. That's why living things have become so specialized at surviving.