My son David, who is a Maths teacher, was discussing with me the probability of dealing two identical hands from a pack of 52 cards. It is staggeringly small.
It is calculated as 1/52! (52 factorial). That works out as 1/8.07 x 1067.
8.07 x 1067 is a mindbogglingly huge number, therefore 1/8.07 x 1067 is a staggeringly small probability. In fact you would say it will not happen.
I am a retired Chemistry teacher and that got me thinking.
1. A simple probability
What is the probability of throwing 4 dice and each one turning up 6?
The probability for one dice turning up 6 is 1 in 6
probability = 1/6
The probability for four dice turning up 6 is given by multiplying the probabilities.
probability = 1/6 x 1/6 x 1/6 x 1/6 = 1/64 = 1/1296
This is how the following probabilities are calculated.
2. Protein Chemistry
This is part of the note I used to give my Higher Chemistry classes.
Proteins are chemicals containing the element nitrogen. Proteins are the major structural materials of animal tissue. Proteins are also involved in the maintenance and regulation of life processes.
Amino acids, the building blocks from which proteins are formed, are relatively small molecules which all contain an amino group (NH2), and a carboxyl group (COOH). The majority of amino acids found in proteins are of the type
R represents a carbon side chain which may contain even the elements nitrogen and sulphur.
|Name||R (side chain)|
|Valine||-CH CH3 CH3|
|Leucine||-CH2 CH (CH3)2|
|Aspartic Acid||-CH2 COOH|
|Methionine||-CH2 CH2 S CH3|
Proteins are condensation polymers formed by combining amino acids to form long chain molecules of maybe several thousand amino acid units long. The structure of a section of protein is based on the constituent amino acids. When amino acids join together a peptide link (or amide link) (CONH) is formed and water is eliminated. The peptide link is formed by the reaction of an amine group with a carboxyl group.
There are 20 amino acids that protein is made from.
Proteins can be classified as fibrous or globular. Within proteins, the long-chain molecules may be twisted to form spirals, folded into sheets, or wound around to form other complex shapes. The chains are held in these forms by inter-molecular bonding (eg. hydrogen bonding or dispersion forces) between the side chains of the constituent amino acids.
Fibrous proteins are the major structural materials of animal tissue. The molecules are folded into sheets. Fibrous proteins are found in skin, hair and muscle. Examples include the keratins (in wool, hair and nails), the collagens (in skin and tissue) and the elastins (in lungs and arteries).
Globular proteins are the functional proteins in living organisms. Globular proteins are involved in the maintenance and regulation of life processes and include enzymes and some hormones. Enzymes are biological catalysts and each enzyme has a specific task. The globular proteins have to be soluble in water to function in cells. In an enzyme the protein molecule is coiled and folded in a very specific way which leads to its biological function. The very specific shape allows only a certain substrate (reactant) molecule to fit and react. If the shape of the protein in coiling and folding is altered the enzyme will not work. The protein is said to be denatured. Changes in temperature and changes in pH lead to this denaturing.
That is school Chemistry.
3. Abiotic (or pre-biotic) synthesis of protein
The suggestion by Science is that these amino acid molecules were in some ‘primordial soup’ and managed to join at random to form the larger molecules of life. That takes faith. If you have carried out any form of synthetic Chemistry you will know that conditions have to be incredibly precise for a reaction to take place (eg. concentration, pH and temperature). You have to purify before going on to the next step. You have to extract. You have to make sure you have enough reagent. Mixing a whole heap of Chemicals together just does not work.
So supposing there was this ‘soup’ what is the probability of these amino acid arranging to form a biologically active polypeptide by pure chance.
Insulin is a smaller molecule than an enzyme. It is a hormone made in the pancreas which allows the body to use glucose for energy. It is made from 51 amino acids using 17 of the permitted 20. It must be about the minimum size of polypeptide that can cause a biological response or activity.
What is the probability of each amino acid being in the correct place in the sequence? It has to be exactly in that order to be functional.
From the chain above what is the probability of the first amino acid being glycine (Gly). If there are 17 amino acids it must be 1 in 17 (1/17).
The probability of the second amino acid being isoleucine (Ile) is again 1/17.
It is similar to having a 17 sided dice. The probability is the same as throwing 51 17 sided dice. So the probability of that molecule of insulin having all the 51 amino acids in the order shown is given by –
probability = 1/1751 = 1/5.66 x 1062
That is more than extremely improbable. Just a factor of 10 different from dealing two identical hands from a pack of 52 cards shown earlier!
6. 3. 4-oxalocrotonate tautomerase
4-oxalocrotonate tautomerase is the smallest enzyme in the human body. It is an enzyme that converts 2-hydroxymuconate to the alpha-beta-unsaturated ketone, 2-oxo-3-hexenedioate (that bit of Biology I don’t understand!).
The molecule is formed from 62 amino acids. Assuming all 20 amino acids for life are available. Forming this arrangement of atoms by chance would be calculated in a similar way to shaking 62 20 sided dice.
probability = 1/2062 = 1/4.61 x 1080
That is ridiculous. To give some idea of what 4.61 x 1080 is as a number, it is estimated that the there are between 1078 to 1082 atoms in the known, observable universe. Yet, Scientists say this molecule has formed by chance.
7. Salivary amylase
The enzyme salivary amylase starts the process of starch digestion in the mouth. It breaks starch molecules down into maltose.
Amylase is built up from 496 amino acids.
The probability of the amino acids ending up in the order they are in by chance can be calculated by –
probability = 1/20496
This can not be calculated by the spreadsheet on my computer. It cannot be calculated on my calculator. It could not be calculated on any of the online calculators I tried. The answer is beyond large!
Now that is the probability for only two enzymes and one hormone forming by random joining of amino acids. When you combine probabilities they don’t add they multiply.
There are approximately 1300 different enzymes found in the human cell! Each of these coming about by chance.
Or what about the probability of the pre-biotic evolution of the DNA. It is DNA that dictates the arrangement of the amino acids in the proteins in living cells.
DNA, or deoxyribonucleic acid, is the hereditary material in humans and almost all other organisms. Nearly every cell in a person’s body has the same DNA. Most DNA is located in the cell nucleus.
The information in DNA is stored as a code made up of four chemical bases: adenine (A), guanine (G), cytosine (C), and thymine (T). Human DNA consists of about 3 billion bases, and more than 99 percent of those bases are the same in all people. The order, or sequence, of these bases determines the information available for building and maintaining an organism, similar to the way in which letters of the alphabet appear in a certain order to form words and sentences.
The probability here would be
probability = 1/43,000,000,000 = beyond calculation, beyond possible!
What about the time involved to give these molecules their chance to form.
The age of universe is reckoned to be about 13.8 billion years (if you believe the Science!)
This works out in seconds as
= 13.8 x 1000000000 x 365 x 24 x 60 x 60 = 4.35 x 1017 seconds
Take the smallest of these polypeptides mentioned above. To form insulin by chance allowing one change of its 52 amino acids per second would take 1/5.66 x 1062 seconds (this is the most extreme).
The number of ages of the universe to do that would be
1/5.66 x 1062 / 4.35 x 1017 = 1.30 x 1045 ages.
And planet Earth is even younger at supposedly 4.54 billion years. There is not the time to randomly form just insulin by chance.
Also, it cannot be just one molecule that is formed but a sufficient quantity or concentration must be synthesised for further Chemistry to take place.
10. Avogadro’s Number
An argument that could be put forward is the number of particles involved in collisions of molecules as they react is vast.
Avogadro’s number, number of units in one mole of any substance (defined as its molecular weight in grams), equal to 6.02214076 × 1023. The units may be electrons, atoms, ions, or molecules, depending on the nature of the substance and the character of the reaction (if any).
If presuming a millimole of substance (eg. insulin) is formed there would be 51 x 6.02 × 1020 amino acid molecules colliding. So that should increase the probability.
My Maths is weak but I presume that would reduce the probability for insulin to form by
probability = 1/5.66 x 1062 x 51 x 6.02 × 1020 = 1/5.42 × 1041
That is still a very low probability.
However each of these 6.02 × 1020 insulin molecules with a probability of 1/1.84 × 1040 has to be formed separately. So the term will cancel itself out.
probability = 1/1.84 × 1040 / 6.02 × 1020 = 1/5.66 x 1062
So taking Avogadro’s number into the discussion or calculation has no effect on the final probability.
11. Chiral molecules
12. I have to believe in a Creator.
One argument suggested by Scientists to get round these infinitely high improbabilities is the multiverse model. The idea is that there are many universes. The suggestion is that there are 10500 universes. There is not a shred of evidence for that. David Berlinski asks the questions – is it easier to believe in 10500 other universes or to believe in one God? It has to be God.
(Psalm 8: 3, 4) When I consider thy heavens, the work of thy fingers, the moon and the stars, which thou hast ordained; What is man, that thou art mindful of him? and the son of man, that thou visitest him?
I have found this wee bit of Maths so helpful. After studying Chemistry I struggled with reconciling the model given by Science and the model given by the Bible to explain creation. Part of me swallowed some of the misinformation fed to me by Scientists. Part of me clung to the teaching of my parents. I always believed that Jesus was the Christ the son of the living God.
Those claiming to be Scientific ridicule those that take a different viewpoint. They are considered less intelligent, not as wise, less enlightened and a bit outdated. The current Scientific viewpoint is actually rather narrow minded, exactly what believers in God are accused of being. Surely at least Scientific thinkers should allow others to have a different viewpoint and to consider it. I have become extremely sceptical of the Scientific explanation of how the universe came into being, and I am glad.
(Genesis 1: 1) In the beginning, God created the heavens and the earth.