What is the Probability that Small Proteins would have Formed by Chance in the Primordial Soup? 

by Laurence D Smart B.Sc.Agr., Dip.Ed., Grad.Dip.Ed
Email: laurence@unmaskingevolution.com
Webpage: www.unmaskingevolution.com
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(A) What is the probability that a single protein formed when 100 amino acid randomly joined together?
(1) There are 20 different amino acids that make up the proteins in living things. (Remember, these had to form by chance in the first place).
(2) \ there are 20100 different proteins that can be made from 100 amino acids
(3) This is » 10130 different proteins
(4) \ the probability that a 100 amino acid protein will form by chance = 1 in 10130
(5) This means (according to probability) that to form one specific 100 amino acid protein, 10130 will need to form randomly before the right one forms.
(B) Evolution proposes that many of these proteins came together by chance and then evolved into cells.
(1) But, for a cell to form in the primordial soup:
(i) The many proteins that make it all had to form by chance, &
(ii) Each protein had to form by chance right next to each other
(2) The probability that numerous things will occur by chance is the multiple of each occurring.
(3) \ the chance that 2 different (but correct) proteins form by chance
= the chance of each forming multiplied together.
(4) This = 10130 x 10130 = 10260
(5) So, as a cell is made up of many proteins, it isn't hard to see that the chances are impossible.
viz  10130 x 10130 x 10130 x 10130 x 10130 x 10130 x 10130 x 10130 ............
This is an unimaginable number.
(6) It is now easy to see why Sir Fred Hoyle doesn't believe that life evolved on Earth:
"[T]here are about two thousand enzymes, and the chance of obtaining them all in a random trial is only one part in (1020)2000 = 1040,000, an outrageously small probability that could not be faced even if the whole universe consisted of organic soup." [F. Hoyle & C. Wickramasinghe (1981), "Evolution From Space", J.M. Dent & Sons: London p:24]
(C) How big is a pile of 10130 protein molecules  a bucket full??
(1) What would be the size of the 10130 rubbish proteins that would need to form by chance to create just 1 (one) specific protein of 100 amino acid?
(2) If we average out the weight of the 20 amino acids to 100 Daltons each, then...
....a protein made of 100 amino acids would weigh 100x100 Daltons on average
(3) This = 104 Daltons
(4) \ 10130 proteins would weigh 10130 x 104 Daltons
(5) This = 10134 Daltons
(6) To turn Daltons weight into grams weight, divide by Avogadro's number  1024
(7) \ 10134 Daltons = 10134 ¸ 1024 = 10110 gm
(8) 10110 gm in kilograms = 10110 ¸ 103 = 10107 kg
(9) Let's assume that the density of the proteins is the same as water (ie 1 gm/cm^{3})
(10) So, as there are 1000 gms in a kilogram, then 1 gm/cm^{3} º 10^{3} kg/cm^{3}
(11) \ 10107 kg occupies a volume of 10107 x 10^{3} cm^{3} = 10104 cm^{3}
(12) Now, 1 km^{3} = 105 x 105 x 105 cm^{3} = 1015 cm^{3}
(13) \ the volume of these 10130 proteins = 10104 ¸ 1015 km^{3} = 1099 km^{3}
(14) If these proteins formed a solid cube, each side would measure ^{3Ö }1099 kilometres
(15) This = 1033 km
(16) How long is 1033 km?
If 1 light year = 1013 km, then 1033 km = 1033 ¸ 1013 = 1020 light years
This means that 10^{130} proteins would form a cube
with 10^{20} light year sides
This can be visualized as:
AND THIS IS TO FORM JUST ONE TINY PROTEIN MOLECULE
Imagine how much rubbish protein would need to form by chance over millions of years before the right ones formed (next to each other),  before evolving into the first cell?
SOURCE: Professor F. de Angelis, "The Origin of Life by Evolution: an obstacle to the development of science" (English translation), F. de Angelis: Camucia (Italy) 1995 p:104105