For some this may be a difficult section, so be patient with yourself; you can use your browser and search the web with the words you need explaining, without even leaving your seat. Some parts are even funny!
How to estimate odds
The DNA might be considered a four digit(possibilities) code, being double the computer rate of two digit code
The number possibilities of computers are more familiar; 2,4,8,16,32,64,128,256 being the numbers possible on eight bits, that is a chip with eight terminals which can be off=0 or on =1.
The possibility of changing a single gene data item is one in four, that is it could be changed to any of the four A,T,G, or C, one of which would be no change. If we take two gene data items, any of the first item could be followed by any of the four on the second;
one in sixteen.
So two sets of one in four odds do not add to one in eight, but multiply to one in sixteen.
This often makes the odds in gambling seem so reasonable at first glance: “pick five numbers between one and a hundred”, each part has a one in a hundred chance, they multiply to one in ten billion. (100 x 100 x 100 x 100 x 100 = 10,000,000,000) The punter only thinks in chances in a hundred and chances in five. The same plausibility in suggestion at first and then the numeric system works against the chances for evolution also.
Getting a bit much? What I thought an interesting site, found it during research (it is not otherwise connected with me).
If you are reading on line try: Click to go to visit.
If you are reading a printed copy this is the URL for later: http://micro.magnet.fsu.edu/primer/java/scienceopticsu/poersof10/
Very good visual display on powers of ten.
[additional: These four letters are the initial letters of the amino acids that attach to the DNA helix; Adenine, Thymine, Guanine, Cytosine, so these represent molecules not atoms. The order is not important here.]
Thus; 4,16,64,256,1024,4096,16384,65536; so in eight data items the four possibilities get twice as far as a two digit.
So to by random chance get an eight data item length of DNA say ATGC ATGC is 1 in 65,536.
To follow the sequence;
So to by random chance get a nine data item length of DNA say ATGC ATGC A is 1 in 262,144.
So to by random chance get a ten data item length of DNA say ATGC ATGC AT is 1 in 1,048,576.
So to by random chance get an eleven data item length of DNA say ATGC ATGC ATG is 1 in 4,194,304.
So to by random chance get a twelve data item length of DNA say ATGC ATGC ATGC is 1 in 16,777,216.
Before it gets too boring, note the effect of the 4, every single extra item of data on a DNA line multiplies the "odds (to one)" value by four, that is odds against quadruple per single data item of length.
So what of the number: 473,558,400,000,000,000 seconds since big bang?
One in (seconds from big bang) requires only this many:
ATGC ATGC ATGC ATGC ATGC ATGC ATGC AT or 4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4
1,152,921,505,000,000,000 possible combinations of ATGC in 30 positions (1 in quintillion)
473,558,400,000,000,000 seconds since big bang
Actually it overshoots.
I still find these numbers amazing, a dinosaur part opens its mouth and we could label that half a second with its own unique thirty letter code (sixty letters and we can divide any half a second since the big bang into as many slivers and label). So could any life form exist with only thirty letters of DNA and yet this is one in a quintillion chance of getting it right, multiplying by four for each extra letter added? Life can be very small but how big is that small, as a logical construction?
The big odds in chances question;
Longest DNA is expected to be the human genes and should be published later 2003, Focus magazine May 2003. Should be in the region of 3,000 million base pairs (count as items ATGC ). This is Four repeatedly multiplied three billion times, something like "1" followed by 1,800,000,000 zeroes (estimate only, no I am not doing that in full).
Please note reasoning like this does not of itself disprove evolution, it just makes it less likely. It could still happen but I would not bet on it. Anyway, the person who chooses creation should not feel intimidated by notions that he must accept the fashion of evolution.
[additional: Koran 31 v 27 pen & ink.]
[additional: I have no evidence either way but are the odds even with DNA? There could be things here to question, if disturbed by mutation will it throw one letter more or less often than another? If the system has a bias it may be in favour of life or death.]
Given enough time they said “... a monkey could one day type out the works of Shakespeare”. In the interest's of demonstrable science how far can we test this hypothesis?
The typewriter, nine numeral, twenty-
The monkey's conditions, this monkey can type 500 random keystrokes an hour, twenty four hours a day while fed.
The food, one banana per hour every hour from a stock of 10 to the power 80 (10 times by 10 eighty times). As this is the calculated (by; mathematician G H Hardy) number of protons in the Universe may we consider stock limitless?
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 bananas.
The monkey can now start, there is no need to stop until all the food is eaten, which is:
10 to the power 80
divided by 24 hours times 365.4 days (year's bananas) =8,770 fruits.
10 to the power 80 divided by 8,770 = 1.140 to the power 77 years. 114,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
(a very large number of multiples of the age of the universe, this one old monkey.)
During this time the monkey's output of random keystrokes is:
10 to the power 80 (bananas) times 500 keystrokes hourly rate:
5. to the power 83 or 500,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 random keystrokes
Random keystrokes required to produce Shakespeare:
Remember odds multiply x 30 each letter or space etc. =space
@ ...1 in 30 .. 8.3r keystrokes per minute
1 .. A, @ 1 in 30 A=three and a half minutes
2 .. space, @ 1 in 900 A=hour and forty eight minutes
3 .. P, @ 1 in 27,000 AP=two days six hours
4 .. L, @ 1 in 810,000 APL=sixty-
5 .. A, @ 1 in 24,300,000 APLA =five years six months
6 .. Y, @ 1 in 729,000,000 APLAY=hundred and sixty-
Now is the winter of our
44 letters, 2 commas, 8 spaces, 3 carriage returns (new line) = 57
30 repeat multiplied by 30 for 57 times= 1.57 to the power 84;
1,570,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 random keystrokes
Monkey starves before keying the space after our... all that time and an unfinished cliff-
1] Enter 30, press X, enter 30 & repeat X 30 as required (most calculators)
2] Enter 30 press X twice, then press = as required (scientific calculators)
3] Enter 30 press key marked [XY] enter 57 (algebraic calculators)
Match up your answers with the results A-
The Bard has nothing to fear in monkeys, there could be a problem holding the audience's attention. It really does show the difference in a mind's production and random chance production on an “even playing field”. Did you expect all this at least produced one copy of the complete works of Shakespeare? I did not feel it kind to the animal to exceed 500 keystrokes an hour for one banana and a larger banana source was difficult to source.
1a/ Growth in Nature requires a low mutation rate as there are many cells in an individual life form's make up, or larger life forms would be in a state of constant physiological instability to crisis. Consider the cell quantity of a pod of whales and how long some species remain unchanged over time, before estimating your "one in" chances for mutation. Mitosis & Meiosis may have different rates, pollution might mean mutation rates are high in the present.
1b/ Beneficial must have a fair chance of being on a clean genome.
2/ Species must regenerate to a sufficient number of individuals on average, for the chance of mutations to occur (generations may be added). Thus restarting at one at each mutation insertion. Depends on your estimate; If a mutation is one individual in a million and one mutation in a million is beneficial then one trillion individuals on average per step, while all odds must be available on average only half may be used.
3/ Mutation must occur on the germ line DNA.
4/ Before doing this at home, check quantity of monkeys required to do task in human time frame and ensure sufficient hygienic space for waste products before commencement. Local laws may affect monkey use and waste arrangements.]
Master to apprentice, “No, no, you will never do it like that, never in a million years!”
Thus it is said, "the odds against winning the lottery is vast -
So it goes although the chances against it happening are vast -
First; lotteries follow the laws of odds, properly run etc. Things subject to truly random selection obey those odds. The odds selected for say a national lottery are selected to fit the number of tickets sold to punters, in that case something like the population. The "when it happens" number of multiple winners is often about the same as the "when it happens" draws without a winner. In this case the numbers relate to each other, the chances function in a
Second; the odds in a chance formation of life, exceed the "box". Note the odds on the small section of Shakespeare, is there an approximation to the time available? eg;
Third; The Universe is neither old enough nor big enough for the odds required. The proponents of the lottery paradox fail to mention the scales of numbers.
If for instance the odds for chance formation of a DNA chain were 1 in 15000000000 or near equal to the years since the big bang, then maybe there would be a case.
It is not that simple, there is not one DNA chain but millions and DNA is only one of many complexities of Nature.