How to Calculate the Improbability of Evolution

Posted August 18, 2017 by Amy Wang

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Some attributes of biological life, like irreducible complexity, cannot be explained simply by chance occurrences over a long period of time. Someone once provided this analogy: if you took apart the pieces of a watch, put them in a box, and shook it, you would not get a watch in a million years. Yet, even if everything could be explained by chance, we can still use probability calculations to defend intelligent design as a better explanation than random chance for life as we know it.

Let's first look at how probabilities are used in the debate. To get around the incredible odds of reaching the complexity currently found in biological life, evolutionists argue that even if the probability of forming life is small, given a long enough period of time, it becomes increasingly probable. Suppose you have a one in a million chance of winning the lottery. If you play it only once, your probability of winning is extremely low. However, if you play it a million times, your mathematical probability of winning at least once increases to more than one half:

Probability of winning the lottery for one time = 0.000001
Probability of winning at least once after playing a million times = 1-(probability of never winning for a million times) = 1-(1-0.000001)^1000000 = 1-0.9999991000000=63%.

It would take approximately 693,000 lotteries to break even at 50%. Although winning the lottery is improbable with one lottery, it becomes likely after playing a large number of lotteries. The catch is that you have to live long enough to play that many lotteries.

How Probability Calculations Can Support Intelligent Design

In theory, the idea of low probability events becoming more probable with time is worth considering. However, what if when we actually factor in the total number of lotteries, we find that the probabilities are still extremely small? Then, according to William Dembski, we can use the probability calculation to say that design may be a more plausible explanation than undirected random chance.

The ultimate question is whether we play enough lotteries to make the improbable become probable. Centuries ago, when people believed the universe might have existed for eternity, one might well say there is definitely enough time--infinity is a magic number which makes even extremely low probabilities possible. However, many scientists today support the Big Bang theory, according to which the universe is finite and had a beginning. This discovery makes things a little harder for the evolutionist since we no longer have infinite time. Our question then becomes: How long has the universe existed and does that time provide us with enough lotteries to make life possible?

Intelligent design theorists have studied how to factor in time and chance in probability calculations. In The Design Inference, William Dembski proposes taking into account all possible "lotteries" (e.g., over time and space) to come up with a final probability throughout all of history. Then, 50% becomes the fair dividing point between considering this final probability as evidence for design (less than 50%) or evidence for chance (greater than 50%). In practice, however, we may find the final probability of happening by chance alone is far lower than even 1%, in support of intelligent design.

On top of this, Dembski proposes that the lottery event we win also needs something more than improbability to strengthen the case for design. The rationale is as follows: If you want to allege that a lottery is rigged, it does not help to say that the probability that John Doe wins is miniscule. Whoever wins the lottery, wins with great improbability, but that does not imply someone rigged the lottery. However, if John Doe is the brother of the person running the lottery, then you have a better reason to be suspicious. Furthermore, if the last 10 people who won are relatives of the person running the lottery, that is even greater cause to be suspicious.

The event for which we are calculating the probability cannot just be any event. It needs to be one that indicates purpose and is not well explained by natural means like the regularity of a crystal. Creating a functional protein usable for life is a more purposeful event than creating a random string of amino acids that cannot be used in life. Let's try one sample, hypothetical calculation of the probability of forming one functional protein by chance.

A Sample Calculation: The Probability of Forming One Functional Protein By Chance

QUESTION: What is the the probability of forming just one functional protein by chance alone, after taking in account the entire duration of the universe and the total number of atoms in the universe?

ASSUMPTIONS: Note that numerous assumptions are involved, so one's confidence in the calculation will depend on one's confidence in the assumptions. Feel free to adjust the numbers based on your understanding.

  • Estimated chance for one lottery event:The probability for random formation for just one functional protein has been estimated to be 1 in 1074+45+45or 1 in 10164 (Meyer, 212). Let's suppose that is for one lottery event alone.
  • Estimated total time: The universe's age is estimated to be 14 billion 365-day years = 1.8 * 1016 seconds.
  • Estimated lotteries per second per atom: Let's be generous and assume each atom can be involved in 1 reaction 109 times per second (once per nanosecond) (This is purely hypothetical). If the fastest enzymes catalyze only about a hundred reactions per second, we are being very generous in the number of reactions (lottery events) that can occur, but this still will not help much the case for happening by chance alone.
  • Estimated number of atoms: The number of atoms in the universe has been estimated to be approximately 1080, so let’s assume no more than 1080 concurrent reactions at any point in time.

CALCULATION: We can now come up with a total of 1.8 * 1016 * 109 * 1080 = 1.8 * 10105 lottery events in all of the universe’s history, each with a probability of success of 1 in 10164. There are about 59 orders of magnitude in difference between 10164 and 1.8*10105, so the resulting probability is going to be well below 0.1%! Only if the order of magnitude is about the same can we get a number close to 50%.

Probability of winning the lottery for one time = 1 in 10164
Probability of winning at least once after playing 1.8*10105 times= 1-(probability of never winning for 1.8*10105times) = 1-(1-1/10164)^(1.8*10105) << 1%.

A HUMAN IS MUCH MORE COMPLEX THAN A PROTEIN: If the chance for forming just one functional protein by chance is extremely low, consider how much more improbable it is to form a single cell by chance, which may use 300 to 500 proteins. On top of this, there is another order of complexity to combine cells into multicellular organisms with multiple organs. We also need to leap to compatible male-female reproductive system, a nervous system which enables cognitive thinking, a functional circulatory system, and so forth. On top of this, we have the complexity of 12 meridians of acupuncture, conversions between DC electricity and biochemistry, etc. If chance alone can produce one working cell from scratch, that alone would be amazing, not to mention multi-cellular organisms with multiple systems, all of which are incredibly complex and yet work together in harmony. Are you sure it is not the workings of a master programmer and engineer?

LIMITATIONS: I suppose you could argue that the lottery events are not all independent, so perhaps the probability of winning the lottery the second time around could be better than the first. But how many orders of magnitude of advantage do you think that might give you? In any case, this calculation still gives you a good idea of how amazing it is that we have any functional protein at all.

Remember also that probabilistic arguments, while they provide a useful tool for analysis, are nevertheless based on the infallible Inference to the Best Explanation, which only helps us to make an intelligent guess, but which cannot provide absolute certainty. We cannot rule out the possibility that a natural undirected process was simply lucky. To rule out that possibility, we would still need other supporting evidence like irreducible complexity.

Other Applications for Probability Calculations

Besides the probability of building complex multicellular organisms by chance, probability calculations can also be applied to the following:

  • The fine-tuned cosmic constants: probability by chance estimated at 1 in 10138 (Geisler and Turek, 106)
  • The Bible's prophetic fulfillment against all odds: probability by chance estimated at 1 in 10157 (see the work of Professor Peter Stoner to calculate the odds),
  • The existence of intelligent life (The Adam Equation) and other intelligent civilizations (The Drake Equation) (Whorton and Roberts, 290-292)
  • The complex information in DNA (Note: If Carl Sagan suggested the receipt of a single content-filled message from space would indicate intelligence out there, Gungor asks what about the info in DNA molecule (Gungor, 109-110)?)
  • And so on.


Not only do the cosmic constants appear to be finely tuned for life, but many aspects in biology, such as the information in DNA, also appear to be finely tuned for life, and history appears to be finely tuned for the fulfillment of prophecies about Jesus Christ. What more evidence do we need for a designer of the universe?


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