The Smallest and The Largest Mass of an electron 9.11 x kilograms Diameter of living cell 2 x inches Mass of water.0 x 10 0 grams/cc Distance to the sun 9.3 x 10 7 miles Speed of light 3.0 x 10 8 meters/sec National debt 6 x dollars Evolutionary time 1 x seconds (30 billion years) Number of atoms in a mole 6.02 x Number of electrons in the 1 x conceived universe

Name Name Name Name atto … quintillion atto … quintillion femo… quadrillion femo… quadrillion pico… trillion pico… trillion nano… billion nano… billion micro… million micro… million milli… thousand milli… thousand tenth… ten tenth… ten Powers of Ten

The Evolutionary Premise (I) “…However improbable we regard (an) event …given enough time it will almost certainly happen at least once... Time is in fact the hero of the plot…given so much time, the impossible becomes possible, the possible probable, ad the probable virtually certain. One has only to wait: time itself performs miracles.” Dr. George Wald “…However improbable we regard (an) event …given enough time it will almost certainly happen at least once... Time is in fact the hero of the plot…given so much time, the impossible becomes possible, the possible probable, ad the probable virtually certain. One has only to wait: time itself performs miracles.” Dr. George Wald

Evolutionary Premise (II) “ That which has a probability of one percent in a year, such as a 100 year flood, has a 66 percent chance of occurring in 100 years and a 99 percent chance of occurring in 1000 years” “ That which has a probability of one percent in a year, such as a 100 year flood, has a 66 percent chance of occurring in 100 years and a 99 percent chance of occurring in 1000 years” Dr. K. E. Boulding Dr. K. E. Boulding

Statistical Evaluation (I) For independent, repeated trials of an experiment with two outcomes, success (p) or failure (q), the probability of a number of successes, k, from a number of trials, n, with a probability, p, for each trial is For independent, repeated trials of an experiment with two outcomes, success (p) or failure (q), the probability of a number of successes, k, from a number of trials, n, with a probability, p, for each trial is b = ( n, k ) p k q n - k

Statistical Evaluation (II) The probability of no successes, k=0, is b = q n b = q n Therefore the probability of at least one success is b = 1 - q n b = 1 - q n

For large probabilities, such as Boulding uses, calculations follow his premise, but for small probabilities, “virtually certain” success is an illusion. For p = 0.01 and n =100 & q n = 1 - (.99) 100 = = = 64.3% 1 - q n = 1 - (.99) 1000 = = = 99.9% For p = and n = 100 & q n = 1 - (.999) 100 = = = 9.52% 1 - q n = 1 - (.999) 1000 = = = 63.23%

Protein Translation

A Small Protein Assume a protein of only 100 amino acids (a very small protein). With 20 amino acids the number of possible arrangements of these would be Assume a protein of only 100 amino acids (a very small protein). With 20 amino acids the number of possible arrangements of these would be = (approx) = (approx) For a specific protein, only ONE of these possibilities is possible. For a specific protein, only ONE of these possibilities is possible.

So, the probability of getting a particular protein by random chance is So, the probability of getting a particular protein by random chance is 1 p = = zeros..1 p = = zeros = probability of success = probability of success q = 1 - p = nines q = 1 - p = nines = probability of failure = probability of failure

For repeated random trials, the probability for at least one success would be n  1  1 - q n = 1 -    

To offset this improbability, evolutionary theory demands long time spans. But, even with repetitions a billion times second for 30 billion years the probability is still infinitesimally small, as To offset this improbability, evolutionary theory demands long time spans. But, even with repetitions a billion times second for 30 billion years the probability is still infinitesimally small, as for n = x 10 9 = for n = x 10 9 = q n = 1 - ( nines..) ^ q n = 1 - ( nines..) ^ And, And,  1   1  p = 1 - q n = 1 -   = p = 1 - q n = 1 -   =    