A
Mathematical Explanation of why the Origin of Life by Chance is not possible.

See
companion Excell spreadsheet

In
order for this to make sense, one needs to understand what proteins are made
of and why that is important. Proteins themselves are important because they
are responsible for thousands of chemical reactions that are important for
life. Chemical reactions such as the production of energy from sugar, the
transportation of chemicals from one point to another in the cell, the
structure and integrity of the cell wall, and also the elimination of sodium
from the cell. I won’t spend the time to explain all of these, but take it
on faith that they are all important and without them, the organism cannot
survive.

Proteins
themselves are made up of a string of amino acids. There are 20 amino acids
known that are used in life. Here
is the Wikipedia[1]
description of Amino Acids: “**Amino
acids** (
/əˈmiːnoʊ/,
/əˈmaɪnoʊ/,
or /ˈæmɪnoʊ/)
are molecules
containing an amine
group, a carboxylic
acid group, and a side-chain
that is specific to each amino acid. The key elements of an amino acid are carbon,
hydrogen,
oxygen, and nitrogen.
They are particularly important in biochemistry, where the term usually refers
to *alpha-amino acids*.”

So,
the question is: what are the odds of producing by accident a small, 100 amino
acid, protein. I am assuming there
are abundant amounts of amino acids and a perfect environment for protein
production, even though that will never be the case.

^{1})
. The odds that the next one will
also be left handed is also 50%, but the odds that both of them will be left
handed is 50% times 50% is 0.5x0.5 or 25%, or 1 out of 4 or (1/2^{2}).
Carrying that out for the full 100 amino acid sequence we can calculate that
as 1/100 to the 100^{th} power which is 1/100^{100 }= 1/

But, that is not where the story ends.
In order to make just the right protein, that would fold up in just the
right shape and be effective, the sequence of the amino acids must be perfect.
It is like computer code, the letters in a literary piece, or notes in a
musical score, it must be just so.

^{1}. The odds of
picking the correct one at position 1 & 2 are 20*20 or 400, or 20^{2}.
So the odds of getting all 100 correct are 20^{100}, or 1.27E+130, or
1.27 * 10^{130}.

But, not to pile on, we can’t stop there. The final odds require
we multiply the odds of each part together, the odds of all the amino acids
being left handed multiplied times the odds that all 100 amino in correct
sequence. That calculation is 1.27E+30 * 1.27E+130 = 1.6069E+160.

^{3}), it
equates to a diameter of sphere equaling 1.36E+48 miles[12].
That is much larger than our solar system. Converting
to light years we know light
year is 186,000 (miles per second) * 86400 (seconds per day ) * 365.25 days
per year = 5.86971E+12 miles/light year. In light years, 1.36E+48 miles = (
1.36E+48 / 5.86971E+12) = 2.31E+35 light years in diameter, which is much
larger than the known universe reported at 15,000,000,000 light years. In this
enormous sphere, one would be able to place 3.65E+75 known universes.

[1]
http://en.wikipedia.org/wiki/Proteins

[2]
http://en.wikipedia.org/wiki/Proteins

[3]
http://en.wikipedia.org/wiki/Amino_acid

[4]
http://en.wikipedia.org/wiki/Sickle_Cell_Anemia,_a_Molecular_Disease

[5]
http://www.chemguide.co.uk/basicorg/isomerism/optical.html

[6]
http://en.wikipedia.org/wiki/Amino_acid

[7]
http://en.wikipedia.org/wiki/Amino_acid

[8]
http://www.usmint.gov/faqs/circulating_coins/index.cfm?flash=yes&action=faq_circulating_coin

[9]
http://www.metric-conversions.org/volume/cubic-millimeters-to-cubic-inches.htm

[10]
http://en.wikipedia.org/wiki/Oregon

[11]
http://www.basic-mathematics.com/volume-of-a-sphere-calculator.html

[12]
http://www.rkm.com.au/calculators/calculator-circle-sphere.html

[1]
http://www.chemguide.co.uk/basicorg/isomerism/optical.html

[2]
http://en.wikipedia.org/wiki/Amino_acid

But, that is not where the story ends.
In order to make just the right protein, that would fold up in just the
right shape and be effective, the sequence of the amino acids must be perfect.
It is like computer code, the letters in a literary piece, or notes in a musical
score, it must be just so.

Since there are 20 different possible[6]
choices for amino acids at each position and the odds of picking the right one
at the start, or position 1, are 1 in 20 or 20^{1}. The odds of picking
the correct one at position 1 & 2 are 20*20 or 400, or 20^{2}. So
the odds of getting all 100 correct are 20^{100}, or 1.27E+130, or 1.27
* 10^{130}.

But, not to pile on, we can’t stop there. The final odds require
we multiply the odds of each part together, the odds of all the amino acids
being left handed multiplied times the odds that all 100 amino in correct
sequence. That calculation is 1.27E+30 * 1.27E+130 = 1.6069E+160.

Let’s try to put that number in perspective. Let’ say we marked
a single dime with a red X as the one we were searching for and covered the
State of Oregon to a depth of 1 mile in dimes? Would that represent the odds of
producing a 100 amino acid protein that was all left handed and the correct
sequence? We know that the volume of a dime is 340.106 mm^3[7]
or .020754 in^3[8].
Divide 1 by the volume of a dime and we get 48.1834827 dimes per cubic inch. If
we then multiply that by 12 inches per foot cubed we get the number of dimes per
cubic foot = 48.1834827 * 12 * 12 * 12 = 83,261.05811 dimes per cubic foot.
Multiply that by 5280 (ft per mile) cubed and we get 1.22559E+16 dimes per cubic
mile.The area covered by the State of Oregon is 98,381square miles[9].
The volume of a stack of dimes over
the entire State of Oregon a mile high would be 1.22559E+16
dimes per cubic mile multiplied by 98,381 square miles = 1.20574E+21 cubic
miles. This is not even close to the volume represented by the odds we are faced
with.

So, let’s try to find just how big the volume of dimes it would
take with only 1 being the right one. We know that there are1.22559E+16 dimes
per cubic mile. If we divide the
odds for making our 100 amino acid protein by the number of dimes (each dime
equals one iteration) per cubic mile, we will produce the volume of dimes
represented by odds in cubic miles, 1.6069E+160 iterations / 1.22559E+16 dimes
(iterations)/mile = 1.31E+144 cubic miles. Just
how big is that? Using the formula[10]
(V = (4/3) × pi × r^{3}), it
equates to a diameter of sphere equaling 1.36E+48 miles[11].
That is much larger than our solar system. Converting
to light years we know light
year is 186,000 (miles per second) * 86400 (seconds per day ) * 365.25 days per
year = 5.86971E+12 miles/light year. In light years, 1.36E+48 miles = ( 1.36E+48
/ 5.86971E+12) = 2.31E+35 light years in diameter, which is much larger than the
known universe reported at 15,000,000,000 light years. In this enormous sphere,
one would be able to place 3.65E+75 known universes.

It is actually worse than this because we haven’t included other
variables such as the odds of making a peptide bond rather than other bonds, the
odds of sufficient material being available and the odds of the right conditions
being available.

Casino’s make their money with just a slight edge in the odds. Does anyone think the incredible odds represented above make life by chance possible?

[1]
http://en.wikipedia.org/wiki/Proteins

[2]
http://en.wikipedia.org/wiki/Proteins

[3]
http://en.wikipedia.org/wiki/Amino_acid

[4]
http://en.wikipedia.org/wiki/Sickle_Cell_Anemia,_a_Molecular_Disease

[5]
http://en.wikipedia.org/wiki/Amino_acid

[6]
http://en.wikipedia.org/wiki/Amino_acid

[7]
http://www.usmint.gov/faqs/circulating_coins/index.cfm?flash=yes&action=faq_circulating_coin

[8]
http://www.metric-conversions.org/volume/cubic-millimeters-to-cubic-inches.htm

[9]
http://en.wikipedia.org/wiki/Oregon

[10]
http://www.basic-mathematics.com/volume-of-a-sphere-calculator.html

[11]
http://www.rkm.com.au/calculators/calculator-circle-sphere.html