Well, it's "math" all right, but it models a really stupid scenario which has no resemblance at all to actual biological processes.
That is infinitesmally small.
Yes, and also infinitismally valid as a meaningful model of reality.
On top of *that*, it makes the common ad hoc probability fallacy. Here's an example just like yours about a more familiar process, in order to show how idiotic your math is:
There are 52! (52 factorial, or 52x51x50...x1) possible arrangements to a single deck of cards. Take a deck, shuffle it thoroughly, and spread the deck face up on the table. See that arrangement of cards you ended up with? The odds of getting that exact arrangement are an astronomically small 1 out of 80658175170943878571660636856403766975289505440883277824000000000000 -- it's a miracle!!!Nice try.
Sorry, son, but all your "math" has demonstrated is that it you were randomly shuffling DNA like a deck of cards, the odds of producing someone's specific genome from scratch (and which one? Not counting identical twins, everyone's DNA is *different*) are astronomically low. But so freaking what? No one ever suggested that human life came about by *shuffling*. That's highly idiotic.
Instead, human life has come about via evolutionary processes, which are *not* as pointless and unfocussed as shuffling. And for a taste of just how *much* evolution can speed up things over purely random processes like the one you *incorrectly* try to use as an analogy for evolutionary processes, here's an older post of mine:
For further discussion of the many ways in which your analysis is flawed, see:
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 10195 -- that's a "1" followed by a hundred and ninety-five zeros, or: 1, 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, 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.
Tries <= 1024
Best Critter: "xSeOSEpc3Lm6rnRWnpFYL?QEDY7a67XlfRoJ0e8Len'X'1u'BhdrNqSNaXr7kVjondNozkf2CH9d96SaI?'f43M.CUGJ5XHbqfeR.UJP'tgNP"
Score (0 is best) 101
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
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) 0
Checked 286464 critters in 15 seconds == 19097 tries/sec.
Lesson: Even simple evolutionary processes are *incredibly* more efficient and effective than simple randomness alone. Evolution can *easily* accomplish things which would be *impossibly* improbable by purely random means.
Though misread my intent, you did a nice job of taking my position one step further, and explaining how some more sensible form of evolution than just random shuffling can make dramatic improvements in the rate of advancement.