The Smallest and The LargestThe Smallest and The Largest

• Mass of an electron 9.11 x 10-31 kilograms • Diameter of living cell 2 x 10 - 8 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 10 12 dollars• Evolutionary time 1 x 10 18 seconds (30 billion years)• Number of atoms in a mole 6.02 x 10 23

• Number of electrons in the 1 x 10 80 conceived universe

Name NameName Name

10 10 -18-18 atto …. 10 atto …. 10 1818 quintillion quintillion

10 10 -15-15 femo…. 10 femo…. 10 1515 quadrillion quadrillion

10 10 -12-12 pico…. 10 pico…. 10 1212 trillion trillion

10 10 -9-9 nano…. 10 nano…. 10 99 billion billion

10 10 -6-6 micro…. 10 micro…. 10 66 million million

10 10 -3-3 milli…. 10 milli…. 10 33 thousand thousand

10 10 -1-1 tenth tenth…. …. 10 10 11 ten ten

Powers of TenPowers of Ten

The Evolutionary Premise (I)The Evolutionary Premise (I) “…“…However improbable we regard (an) However improbable we regard (an)

event …given enough time it will almost event …given enough time it will almost certainly happen at least once ... Time certainly happen at least once ... Time is in fact the hero of the plot…given so is in fact the hero of the plot…given so much time, the impossible becomes much time, the impossible becomes possible, the possible probable, ad the possible, the possible probable, ad the probable virtually certain. One has only probable virtually certain. One has only to wait: time itself performs miracles.” to wait: time itself performs miracles.” Dr. George Wald Dr. George Wald

Evolutionary Premise (II)Evolutionary Premise (II)

““That which has a probability of one That which has a probability of one percent in a year, such as a 100 year percent in a year, such as a 100 year flood, has a 66 percent chance of flood, has a 66 percent chance of occurring in 100 years and a 99 percent occurring in 100 years and a 99 percent chance of occurring in 1000 years”chance of occurring in 1000 years”

Dr. K. E. BouldingDr. K. E. Boulding

Statistical Evaluation (I)Statistical Evaluation (I)

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

b = (n, k ) p k q n - k

Statistical Evaluation (II)Statistical Evaluation (II)

The probability of no successes, k=0, isThe probability of no successes, k=0, is

b = q b = q nn

Therefore the probability of at least one Therefore the probability of at least one success issuccess is

b = 1 - q b = 1 - q nn

For large probabilities, such as Boulding uses, For large probabilities, such as Boulding uses, calculations follow his premise, but for small calculations follow his premise, but for small probabilities, “virtually certain” success is an probabilities, “virtually certain” success is an illusionillusion..

For p = 0.01 and n =100 & 1000For p = 0.01 and n =100 & 1000 1 - q n = 1 - (.99) 100 = 1 - .36603 = 0.634 = 64.3% 1 - q n = 1 - (.99) 1000 = 1 - .00004 = 0.99996 = 99.9%

For p = 0.001 and n = 100 & 1000For p = 0.001 and n = 100 & 1000 1 1 - q n = 1 - (.999) 100 = 1 - 0.9048 = 0.0952 = 9.52% 1 - q n = 1 - (.999) 1000 = 1 - 0.3677 = 0.6323 =

63.23%

Protein TranslationProtein Translation

A Small ProteinA Small Protein

Assume a protein of only 100 amino acids (a Assume a protein of only 100 amino acids (a very small protein). With 20 amino acids the very small protein). With 20 amino acids the number of possible arrangements of these number of possible arrangements of these would be 20would be 20100100..

2020100100 = 100 = 100130130 (approx) (approx)

For a specific protein, only ONE of these For a specific protein, only ONE of these 100100130130 possibilities is possible. possibilities is possible.

So, the probability of getting a particular So, the probability of getting a particular protein by random chance is protein by random chance is

11 p = ------ = 0.00000.....130 zeros ..1 p = ------ = 0.00000.....130 zeros ..1

10 10 130130

= probability of success= probability of success

q = 1 - p = 0.99999....130 nines q = 1 - p = 0.99999....130 nines

= probability of failure= probability of failure

For repeated random trials, the For repeated random trials, the probability for at least one probability for at least one

success would besuccess would be

n

1 1 - q n = 1 - 1 - ------- 10 130

To offset this improbability, evolutionary theory To offset this improbability, evolutionary theory demands long time spans. But, even with demands long time spans. But, even with repetitions a billion times second for 30 billion years repetitions a billion times second for 30 billion years

the probability is still infinitesimally small, asthe probability is still infinitesimally small, as

for n = 10for n = 10 18 18 x 10 x 10 9 9 = 10 = 10 2727

1 - q1 - q n n = 1 - (0.999.....130 nines..) ^ 10 = 1 - (0.999.....130 nines..) ^ 10 2727

And,And, 1 1 10 102727

p = 1 - qp = 1 - q n n = 1 - = 1 - 1 - ------- 1 - ------- = 10 = 10 -103-103

10 10 130130