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The Old Improbability Probability Problem

by Paul Smith Version 2 - 15 Jan 2007

We see them over and over .... this or that could not possibly have happened because the improbability is just too great. Usually these are based on very restrictive "all-at-once-out-of-nothing" linear calculations where the errors involved are multifold and pervasive.

First and foremost, it does not matter what is being modeled by any mathematical calculation, whether probability or anything else: math is not reality, and the calculation is a mathematical model of reality and not the reality itself. When a model fails to replicate (model) reality it is not reality that is at fault but the mathematical model. When a hurricane prediction program crashes because it can't model the first hurricane in the South Atlantic on record, the meteorologists don't go out to the hurricane and say "you can't be here, our model does not allow you to be here" ... they fix the model by looking for and taking out the failed assumptions (ie - that all hurricanes are north of the equator). When a model fails to model reality it is a good indication that some aspect of reality has been missed in the model.

Usually these calculations take the form of calculating the probability that an organic molecule could form from raw materials. Without discussing any particular example the errors involved usually include:

  1. The calculation fails to correctly calculate the probability of forming a single linear chain. Whether that chain represents reality or not, the calculation used artificially inflates the improbability by only calculating one possible unit by unit process. Thus you see calculations that keep factoring the improbability, such as the formation of a protein with 200 amino acid bonds usually calculated as (1/20)+200 = 1/(1.6x10+260). The proper calculation is based on the probability that each link cannot form. Let us assume a 5 bonds between 6 amino acids: the {creationist\IDist\etcist} calculation would be
    (1/20)+5 = 0.0000003125 or 1 in 3,200,000
    The proper calculation is a little more complex as the probability changes at each step:
    p1 = 1-p{NOT}1 = 1-{1-(1/20}+1 = 0.0500 or 1 in 20.0000 p2 = 1-p{NOT}2 = 1-{1-(1/20}+2 = 0.0975 or 1 in 10.2564 p3 = 1-p{NOT}3 = 1-{1-(1/20}+3 = 0.1426 or 1 in 7.0114 p4 = 1-p{NOT}4 = 1-{1-(1/20}+4 = 0.1855 or 1 in 5.3910 p5 = 1-p{NOT}5 = 1-{1-(1/20}+5 = 0.2262 or 1 in 4.4205 p = p1xp2xp3xp4xp5 = 0.0500x0.0975x0.1426x0.1855x0.2262 p = 0.00002917 or 1 in 34,282.26
    This difference may not seem that great, but as you keep extending the calculation the value for pn gets closer and closer to 1.0. If we assume a protein with 51 bonds between 52 amino acids all in one particular order, where each letter represents one of 20 amino acids, and the resultant calculation by {creationist\IDist\etcist} is
    p = (1/20)51 = 4.44x10-67 or 1 in 2.25x10+66
    When done by the proper method above the result is
    p = 5.39x10-13 or 1 in 1.85x10+12
    Which, while still large is significantly "more likely" than 1 in 2.25x10+66. In fact it is 1.21x10+54 times more likely. And the longer such calculations are extended the closer the error gets to the {creationist\IDist\etcist} number. When carried out for 200 bonds the result is 1 in 7.62x10+12, or almost a sure thing compared to 1 in 1.6x10+260. Such false {creationist\IDist\etcist} calculations do not model reality in any way.
  2. The calculation fails to account for the known pre-existing molecules used in the formation of life that are found throughout the universe, and this failure means the calculation with creation-all-at-once including these molecules is unnecessarily extended downward, starting with too much simplicity.
  3. The calculation fails to account for the fact that the first life need not be as complicated as a modern cell, that the minimum configuration is much simpler as shown by the LUCA studies. This failure means that the calculation is unnecessarily extended upward, ending with too much complexity.
  4. The calculation fails to account for combinations of groups of such molecules in smorgasbord fashion instead of in assembly line fashion all at once all from nothing. And further, that all those "failed" experiments are still available to be cut and reassembled into new experiments without having to go through all the preliminaries. It fails to account for actual combination process as used in natural assembly of large organic compounds. Amino acids are assembled into larger molecules like peptides and not from extending amino acids by adding atoms. This failure means that all the ways to reach the final necessary combination are not included and thus it unnecessarily excludes possible combination methods.
  5. The calculation fails to recognize that other solutions with different lengths and compositions could also be valid. If you don't know what the possibilities are you can't calculate the probabilities that a possible solution will occur.The probability of winning a lottery by any one ticket is extremely low, but the probability that the lottery will be won is extremely high. How do you reconcile these two very disparate probabilities? By knowing that any one of the millions of tickets is a valid winner if picked. To show that this is not the case for the calculations mentioned (ie -- in order to say "1 out of") you have to show that no other combination works of all the other probabilities. There are several different known forms of hemoglobin, all of which do the job of transporting oxygen in the blood, and thus the probability is high that there are other versions that will work as well. Scientists have also manipulated an organism successfully to make it produce an unnatural amino acid, one that does not occur naturally, thus demonstrating that there are other "solutions" than the ones that happen to be used in life as we know it. It could well be that 1 in a million "solutions" of the possible combinations would work, and that the probability would then reduce to 1 in 106. This calculation has not been done and is not included, unnecessarily excluding possible solutions from the probability calculation.
Finally, whether a valid calculation could be made or not is ultimately irrelevant. We are talking about an event that either (a) has occurred or (b) has not occurred, and in the event that it HAS occurred the probability that it DID occur is 1.0 - it cannot un-occur. The difference between improbable and impossible is vast:

improbable = 1/(small number >0) <<<<<< 1/0 = impossible

Thus any calculation of the improbability of a thing occurring - no matter how small - is not proof of any impossibility that it did not in fact occur. It could well be that this is the only planet in all the universe that has life on it because it is a very improbably event. Ultimately this probability argument is one from ignorance and incredulity - both logical fallacies.

When it comes to modeling the possibilities of life beginning from molecules at the dawn of life on earth, we don't have the information to know what combinations would result in a replication system that becomes life, life that evolves into all the diversity that we see today. Without the data on the possiblities you cannot compute the probabilities. For example: I hold three faceted solids in my hand, the sides may or may not be regular or equal, the number of sides may or may not all be the same on all three, the markings may or may not all be the same on all three: What is the probability that I will throw a "7" when I throw these objects onto the table?

Please supply your computations.

Enjoy

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Notes:

  1. This is an essay and as such represents the opinions of the author. You can e-mail comments to me at RAZD8@yahoo.com)
  2. Where possible, I have tried to follow the standard academic procedure for citing online publications, where if you last accessed this page on 16 Jan 2007, and used this version, you would cite this as:
    Smith, Paul "The Old Improbability Probability Problem" razd.evcforum.net, Version 2, updated 15 Jan 2007, accessed 16 Jan 2007 from http://razd.evcforum.net/(this url).html
  3. Also see formal MLA style referencing.

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