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The Mathematical Impossibility of the Theory of Evolution

By David Holden

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Also See   Scientific Facts in The Bible       &     The Case For Christianity

How Did We Get so Many People in Such a Short Time?   (Below)


The Probability of an Event Occurring
My interest in the probability of an event occurring goes back to the days when I sold various insurance policies. The annual amount a person pays for house insurance is calculated after various factors are considered, for instance, the value of the house, the age of the house, whether it is constructed of timber or brick, and whether it is in a high risk fire or flood zone. A good car will cost more than the house to insure because it is exposed to greater risk. If you should also own a good motorbike, it will cost more per dollar value than the car to insure because of the greater risk of damage or theft.

Insurance companies employ a person called an actuary to calculate through statistical and mathematical means the probability of an accident occurring, and the amount that should be charged to the customer for the insurance policy. It is the belief of this author that life is too complex to come into being by accident, so I will not attempt to calculate the possibility of various components coming together accidentally to create life - I will leave those calculations to the mathematicians who have the belief and the means. It is my aim in this paper to calculate the possibility of a hypothetical, very simple 200 part creature, coming together by accident. But first, we will consider the complexity of earth's simplest creatures.

How Complex is Life?
Professor Ilya Prigogine has this to say about the complexity of the machinery within all organisms which must work correctly in order to sustain life. "But let us have no illusions. If today we look into the situations where the analogy with the life sciences is the most striking - even if we discovered within biological systems some operations distant from the state of equilibrium - our research would still leave us quite unable to grasp the extreme complexity of the simplest of organisms." (Professor and Director of the Physics Department, Universite Libre de Bruxells at the time of his statement).

Ernst Chain (world famous biochemist) makes the same point in another way. "I have said for years that speculations about the origin of life lead to no useful purpose as even the simplest living system is far too complex to be understood in terms of the extremely primitive chemistry scientists have used in their attempts to explain the unexplainable that happened billions of years ago. God cannot be explained away by such alive [sic] thoughts."

There Has to Be A God
"Today, Professor Sir Fred Hoyle, an agnostic of Christian background, and Professor Chandra Wickramasinghe, an atheistic Buddhist, are changed men. They are both believers" [But not true Christian believers].

    "'It is quite a shock,' says Wickramasinghe, Sri Lankan born Professor of Applied Mathematics and Astronomy at University College, Cardiff. ‘From my earliest training as a scientist, I was very strongly brainwashed to believe that science cannot be consistent with any kind of deliberate creation. That notion has to be very painfully shed. I am quite uncomfortable in the situation, the state of mind I now find myself in. But there is no logical way out of it.'

"What convinced both men were calculations they each did independently into the mathematical chances of life starting spontaneously. When each had finished, they looked at the answer almost in disbelief. Each found that the odds against the spark of life igniting accidentally on Earth were staggering - in mathematical jargon ‘10 to the power of 40,000. If you write down the figure ‘1' and add 40,000 noughts after it, you have the figure." A figure with fifteen zeros is usually considered to be very large.

How Long Does it Take?
Let's do a simple maths exercise. If I had a bowl of alphabetical soup with just the letters A and B floating around on the top in such a way that a different arrangement of letters was formed on the surface every second, so that AB formed in the first second, then BA in the next. I would have to wait just two seconds to cover all of the different possibilities which are AB or BA.

If I enter just one more letter, the letter C. The time needed to go through all of the different combinations would be six seconds. One more letter will increase the time needed to twenty-four seconds. From the illustration below, it can be seen that as each letter is added, there is a marked increase in the time needed to go through all of the possible combinations.

    BA two seconds

    CBA six seconds for the above group

When the number of letters is increased from three to four, there is a large increase in the number of combinations possible.

    (I will run the rest of the combinations side-by-side to save space) ABDC CBAD ACDB CADB ADBC CBDA ADCB CDAB BACD CDBA BCAD DABC BADC DACB BCDA DBAC BDAC DBCA BDCA DCAB DCBA

There are twenty-four (24) combinations in the above group, therefore twenty-four seconds are required at a rate of one per second.

The above group increases five-fold when we add just one more letter to the group.

It will take 120 seconds (five times the previous number) to go through all of the above 120 combinations of the five letters ABCDE.

If the letter F is added, the time taken to go through all of the combination of letters will increase to 720 seconds. When the letter G is added, the time increases to 5,040 seconds. With each additional letter, you multiply the previous result by the new number of letters.

To calculate the time need to go through all of the combination of letters when the letter H is added (total of eight letters), you multiply 5,040 seconds by eight, which gives 40,320 seconds.
See the table below, the first number in brackets is the number of letters used:

    (2) 2 seconds
    (3) 6 seconds
    (4) 24
    (5) 120
    (6) 720
    (7) 5,040
    (8) 40,320
    (9) 362,880
    (10) 3,629,900
    (11) 39,916,800
    (12) 479,001,600
    (13) 6,227,020,800
    (14) 8,717,829,120
    (15) 1,307,674,368,000
    (16) 20,922,789,888,000
    (17) 355,689,428,096,000
    (18) 6,402,373,705,728,000
    (19) 121,645,100,408,832,000
    (20) 2,432,902,008,176,640,000 Seconds with twenty letters.

As there are 31,556,925 seconds in a year, it would take more than 77 billion years (77,095,661,512 years) to go through all of the combination of letters.

NASA scientists believe that the smallest number of parts possible in an organism considered to be living is 400, which must be in the correct order. This number is probably very much underestimated, but let's cut the number in half, so that we have just 200. Even with this very small number of parts, it would take a staggering 788,657,867,364,791x10^360 seconds (After the number 1 in 791, we must add 360 zeros) to try all of the possible combinations. We will round the above number down to 788x10^372 seconds.

The symbol ^ = exponential, 10^3 = 10x10x10 = 1,000 and 10^4 = 10x10x10x10 = 10,000. It saves writing a lot of zeros.

How many combinations can we get through in the time the universe has been in existence?

Evolutionists put the age of the universe at around 30 billion years. That is 9.46x10^17 seconds. We will round that number up to 10^18 seconds. In 30 billion years, we will get through 10^18 combinations of letters at the rate of one new combination per second. But we need to go through 788x10^372 combinations. So let's speed things up a bit.

There are 10^80 electrons in the universe - larger than the number of atoms. By way of illustration, we will use this number as the maximum number of parts to work with. Now let's divide all of the electrons in the universe into groups of 200. This will give us 5x10^77 groups to work with. This means we can get through all of the possible combinations 5x10^77 times faster. However, even with this unrealistic situation, we can only get through 10^18 x 5x10^77 = 5x10^95 combinations. Well short of the number we need to get through.

So let's speed things up further. We will increase the speed of change throughout the whole universe from one trial per second, to one billion per second. Also, we will increase our time limit from 30 billion years, to 300 billion years.

    300 billion years 10^19 seconds
    Trials per second 10^9
    Electrons /200 5x10^77 groups of 200
    Total trials 5x10^105

Even when we work at the staggering rate of one billion trials per second throughout the whole universe for a period of 300 billion years, we can only achieve 5x10^105 combinations. That is well short of the 788x10372 combinations needed to be sure that we can arrive at the correct combination to start our very simple form of life. In fact, impossibly simple at just 200 pieces.

Earth to star line
Let's draw an imaginary progress line to visualise how far we have gone with all of the electrons in the universe changing position one billion times per second for 300 billion years. We will use a very long line, it will extend from the earth to the nearest star, Alpha Centauri (or Proxima Centauri) which is situated 4.3 light-years from the earth.

Light travels in a vacuum at 299,792,458 metres per second. We will round this number up to 300x10^6 metres per second. There are 31,556,925 seconds in a year. In 4.3 years, 135,694,777 seconds. We will round that number up to 136x10^6 seconds.

The length of our line will be 136x10^6 seconds x 300x10^6 metres = 408x10^14 metres.
Because we have rounded up both numbers, this has the effect of extending the line just beyond the star Alpha Centauri. To travel the length of our line (408x10^14 metres) in 4.3 years or less, we need to have a velocity of at least 300,000 kilometres (300x10^6 metres) per second.

    Length of line
    408x10^11 kilometres
    408x10^14 metres
    408x10^17 millimetres
    408x10^20 microns

Distance travelled on progress line
To calculate the fraction of the distance along the line that we have moved, we need to divide the number of combinations completed 5x10^105, by the number of combinations we need to complete the task, 788x10^372 which represents the end of the line at 408x10^20 microns.

In summary:
1 divided by 788x10^372 (1/ 788x10^372) = the beginning of our journey along the line.
788x10^372 divided by 788x10^372 = 1, the end of the line at 408x10^20 microns.

Please note from the table below that as each number of trials is reduced by one tenth, our position along the line is also reduced by one tenth.

    No. of trials
    788x10^372 End of line
    394x10^372 half way along progress line.
    788x10^371 one tenth (10^1)
    788x10^370 one hundredth (10^2)
    788x10^369 one thousandth (10^3)
    788x10^368 one ten thousandth (10^4)
    788x10^367 one hundred thousandth (10^5>
    788x10^366 one millionth (10^6)

Please grab the electron microscope!
As can be seen from the above, 788x10^366 completed combinations is just one millionth of the combinations that we are aiming to achieve. But we have completed only 5x10^105 combinations. Let's increase this number for the benefit of the evolutionist and to simplify our next calculation to 788x10^105.

Our calculation is 788x10^105 divided by 788x10^372 which equals 1/788x10^267 as the fraction of the distance along the line. The bigger the exponential number, the smaller the fraction or distance along the line. If we continue the table above we have:

    No. of trials
    788x10^366. Position on line = one millionth (10^6)
    788x10^365. Position on line = one ten millionth (10^7)
    788x10^364. Position on line = one hundred millionth (10^8)
    788x10^105. Position on line = (10^267)

With a fraction less than 1/10^20, the distance covered is less than a micron, which is one thousandth of a millimetre, but the fraction we have is 1/10^267. That means that with all of the electrons in the universe moving at the rate of a billion trials per second for 300 billion years, we have not moved beyond one atom on our astronomically long line. We must also consider the fact that a 200 part system is ridiculously simple in comparison to the simplest of living organisms.

The step-by-step method
Let's consider the chance of putting our simple 200 part system together in the correct order through a step-by-step approach. Unfortunately for the evolutionist, this only makes matters worse. The calculation used to arrive at the possible number of combinations through this step-by-step approach is as follows:

    2!+3!+4!+5!+6! ... + 200!
    That is: 2+6+24+120+720+5,040+40,320+362,880+ 3,629,900+39,916,800 ... +200!

From the above, we can see that after just ten steps, we will arrived at the number 43,955,812 With the more straightforward approach, the number arrived at with ten different letters is: 3,629,900.

The symbol "!" represents factorial. The factorial of each number must be added up all of the way through to the number 200. Obviously we will arrive at a number much larger than the number 788x10^372.

Hopefully by now, it will be understood that even a hypothetically simple form of life can not come into existence by chance random processes. But for the sake of the few diehards, we will persist with our hypothetical simple bug. Let's take a giant leap of faith and say that after 600 billion years, we finally have our simple form of life. That is well short of the time needed to go through all of the combinations as explained earlier. Another problem for the evolutionist is the fact that in less than 100 billion years, all of the stars in the universe will run out of fuel and die. Without the intervention of God, our star, the sun, will remain in its present condition for only 5 billion years before expanding and dying. But let's ignore this problem; we have our bug (simple 200 part form of life) in just 600 billion years.

Because it is a simple form of life, it can not reproduce.

Reproduction is very complicated requiring many thousands of pieces in the correct order before it will work. To help the evolutionist, our bug will have a very simple form of reproduction. If the reproduction mechanism were simply a matter of a couple of letters being in the correct order, such as AB or BA, then we would have reproduction after just two bugs have come into existence. On the law of averages, the first bug would fail, and the second bug would succeed in producing offspring. If reproduction requires ten parts, then we would go through 3.6 million bugs before we could come up with a successful bug which had the ability to reproduce.

We will limit the number of pieces in the reproduction system of our bug to just 200. We now proceed as follows with many concessions in favour of the evolutionist:

    • We divide all of the electrons in the universe into groups of 200
    • All of the electrons in the universe change position at a rate of one billion trials per second
    • After 600 billion years, we allow that a bug is formed.
    • The first bug fails to reproduce, so the above situation is continually repeated.
    • After the required number of trials, a bug succeeds in reproducing.

The number of trials
The number of trials or failed bugs that we would need to go through with our simple 200 part reproduction system can be mathematically worked out to be 788x10^372 - as explained earlier. That's 788 with 372 zeros after it.

Life can not overcome such staggering odds. We have not even considered plant life in which we could use the above math model to explain the impossibility of its coming into existence by chance anywhere in the entire universe.

The complexity of the DNA molecule
All of life, from the very simplest, to the human being, is a wonder of God's creation. Let's consider the amazing complexity of the DNA molecule. "DNA contains its information in the sequence of four chemical compounds known as nucleotides, abbreviated C,G,A,T. Groups of three of these at a time are ‘read' by complex translation machinery in the cell to determine the sequence of 20 different types of amino acids to be incorporated into proteins. The human DNA has some three billion nucleotides in sequence. ... The amount of information in the three billion base pairs in the DNA in every human cell has been estimated to be equivalent to that in 1,000 books of 500 pages."

We don't find mathematical support for the spontaneous generation of life through various chemicals accidentally bumping into each other. However, we do find mathematical support for the biblical claim that man has been on the earth less than 10,000 years.

The population of the world
If we go back one thousand years, the population of the world was 275 million (The Encyclopedia Britannica puts the figure at 300 million.) In the year 1 AD it was 138 million according to the World Book Encyclopedia.

If there were 300 million people on earth at the time of Christ, this requires a population growth rate of only 0.75% since the great Flood at around 2,500 BC, or a doubling time of 92 years. Dr. Don Batten makes the following point. "What if people had been around for one million years? Evolutionists claim that mankind evolved from apes about a million years ago. If the population had grown at just 0.01% per year since then (doubling only every 7,000 years), there could be 10^43 people today - that's a number with 43 zeros after it." There are not enough human remains to indicate that man has been on the earth for one million years.

For Details See Below..

End Notes
1. ‘Can thermodynamics explain biological order?', Impact of Science on Society, vol. 23 (3), 1973, p.178. (From "The Revised Quote Book", Creation Science Foundation, 1990, p. 6).
2. As quoted by R.W. Clark, in The Life of Ernst Chain: Penicillin and Beyond, Weidenfeld & Nicolson, London, 1985, p.145. (From "The Revised Quote Book", Creation Science Foundation, 1990, p. 6).
3. "Sunday Mail", 20 September 1981.
4. Sun, "World Book Encyclopedia", CD, 1997.
5. "Creation Ex Nihilo", Dec. 1996, p. 21, 22.
6. World, "World Book Encyclopedia, Chicago, 1974, Vol. 21, p. 344f.
7. Trends in World Population, "Encyclopaedia Britannica", CD 2000
8. Don Batten, B.Sc.Agr. (Hons), Ph.D. "Creation", June-Aug. 2001, p. 52-55.


How Did We Get so Many People in Such a Short Time?
by Jonathan Sarfati (answersingenesis.org)

To work out how quickly a population can grow, it’s very important to understand exponential growth. Starting from eight people after the Flood, the population would have to double only 30 times to reach 8.6 billion. Now there is a well-known ‘Rule of 72’, which says divide 72 by the percentage growth rate to get the time required for doubling.* E.g. if inflation is 8% p.a., then in 72/8 = 9 years, the cost of living will have doubled.

So what is a realistic growth rate? The Encyclopedia Britannica claims that by the time of Christ, the world’s population was about 300 million. It apparently didn’t increase much up to AD 1000. It was up and down in the Middle Ages because of plagues etc. But may have reached 800 million by the beginning of the Industrial Revolution in 1750—an average growth rate of 0.13% in the 750 years from 1000–1750. By 1800, it was one billion while the second billion was reached by 1930—an average growth rate of 0.53% p.a. This period of population growth cannot be due to improved medicine, because antibiotics and vaccination campaigns did not impact till after WWII. From 1930 to 1960, when the population reached three billion, the growth rate was 1.36 % p.a. By 1974, the fourth billion was reached, so the average growth rate was 2.1% from 1960 to 1974. From 1974 to 1990, when the mark hit five billion, the growth rate had slowed to 1.4%. The increase in population growth since WWII is due to fewer deaths in infancy and through disease.

If the average growth rate were a mere 0.4 %, then the doubling time would be 180 years. Then after only 30 doublings or 5400 years, the population could have reached over eight billion.

If you want something more rigorous, there are standard mathematical formulû that can be used to calculate population growth. They must include birth and death rates as well as generation time. The simplest formula involves just a constant growth rate:

N = N0 (1 + g/100)t

where N is the population, N0 is the initial population, g is the percentage growth rate per year, and t is the time in years. Applying this formula to the population of eight surviving the Flood, and assuming a constant growth rate of 0.45% p.a. and 4500 years:

N = 8 (1.0045)4500 = 4.8 billion people.

Of course, the population growth hasn’t been constant, and would have been very fast just after the Flood. Thus this formula by itself cannot be used to prove a young earth. Look up the website article Young World Evidence—there is a section on population—if the world’s population had been in the millions for 100,000 years, then where are all their bodies?


More precisely, the formula is: doubling time = 100 ln2/g, where ln2 is the natural logarithm of 2 (0.693) and g the percentage growth rate. So it would be slightly more precise to use a ‘Rule of 69’, but 72 is chosen because more numbers divide evenly into it, and it is good enough for an approximate rule of thumb.


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