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Creationist site Creation.som cites a commenter who complains that biologists ignore his arguments:

Then I try and help [evolutionists] understand the mathematics and logistics of creation and evolution. I tell them that evolution IF we take only the change of evolution then the chance of it being successful for one body type is around about 1 in 1 billion Trillion, and even in the time given in the secular graph of time of the earth cannot reach that 1 in 1 billion trillionth chance.

My question is specifically about that "math and logic" and that "1 in 1 billion trillionth chance" I have seen my fair share of creationist arguments but this math part is new to me.

Is it true that the Earth is too young for evolution to have reached its current outcomes?

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    It's hard to understand what the "1 in 1 billion trillionth" claim is based on, but I suspect it's the same logical fallacy as saying "I picked a random number between 1 and 1,000,000,000,000. The number I got was 307,984,462,932. The chance of getting that exact number is miraculously unlikely - just a 1 in 1,000,000,000,000 chance. Therefore it's a miracle". I forget the name of the fallacy, but it's based on treating one random outcome as an unlikely coincidence, when actually it only coincides with itself. It assumes the human body was some pre-destined goal, not just where we ended up. – user568458 Mar 26 '16 at 21:26
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    Here's an example newscientist.com/article/… notice how they fail to refute the improbability – D J Sims Mar 26 '16 at 21:35
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    Did you read the article, in particular the analogy to shuffling a deck of cards? If you pick up any shuffled deck of cards, the chance of it having that exact order is even more unlikely than "1 in 1 billion trillionth", it's around 1 in 10^68 (1 then 68 zeros). But it had to have some order. Why not this order? The other possibilities are just as unlikely. It's only an implausible miracle if you assume that this random order of cards (or, this particular body type with its hairy bits and dangly bits and appendixes) is somehow the "right" one, and not just the one we got. – user568458 Mar 26 '16 at 21:53
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    The great fallacy here is a misunderstanding of how evolution works, specifically the belief that evolution is a purely random process. That belief misses the role of natural selection, which is what "drives" the process. – Mark Mar 26 '16 at 22:38
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    @Mustang: If you have a notable claim to support that position, it might make a good Skeptics question. If you don't, it might make a good discussion in chat. However, it is a can of worms too large to be opening in the comments section. – Oddthinking Mar 27 '16 at 1:10
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This is a fairly common objection to evolution, that appears in various forms. There is a good answer here. It can be generalised to this:

Given a biological structure made up of a specific arrangement of a large number of substructures how likely is it that this particular arrangement could be formed by picking the substructures at random?

Where the biological structure can be - for example - a human, a protein, or a cell. The substructure might be the smallest possible (atom for humans) or the level just below (amino acid for protein). Let's choose a particular example :

Given a protein made up of a folded chain of 200 amino acids how likely...

So given an alphabet of 20 amino acids, we have a 1 in 20 to the power 200 or 1-in:

1.606938044258990275541962092341162602522202993782792 × 10^260

according to Wolfram Alpha. This is because you can choose 1 out of 20 for the first position, 1 out of 20 for the second, and so on. This quickly gives you a very large number.

Now the obvious objection to all this is simply that evolution does not work this way. Every cell in your body has a parent, and those parents had grandparents, and so on all the way back to the fertilised egg. That egg (zygote) formed from a cell from your mother and a sperm from your father, and onward back through time.

So too with any biological structure; it had previous versions, which had previous versions, which had ... you get the picture. There is a lineage therefore for any structure that is just not addressed by this idea of random formation.

However, there is a more subtle problem with the "evolution is mathematically impossible" idea. It is in the specific arrangement part of the generalisation. We can't talk about how possible (or impossible) a structure is unless we know how many such structures there are. I'm talking here about the ratio of functional to nonfunctional structures.

For example, if I could look at a haemoglobin molecule in my blood it would appear very well designed for its particular function - using haem cofactors to bind and release oxygen. However, this is not the only design! You might have a haemoglobin with a slightly different sequence, which also does the job of binding oxygen. In fact it might do it slightly better than mine.

More broadly, a large number of sequences bind to haems and - although they may do a bad job of it - may be able to transport oxygen through blood. Which is where we come back to the idea of lineages. A previous version of my haemoglobin may well have been worse at its job but it did do something and that something was selected for by evolution.

So in conclusion, evolutionary processes pick their way through the configuration space of all possible structures. They don't just jump to one particular point in that space.

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    Welcome to Skeptics! This is an answer would be improved by focussing on quoting the arguments made in some of your references, and not attempting to do your own speculative calculations, that haven't been peer reviewed. – Oddthinking Mar 27 '16 at 1:13
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    Another point here is that evolution - or life, if you want - is not a serial computation. It is massively parallel, with variations being tried by billions of individuals. The only estimate I found is something like 5*10^30 individual organisms existing at any one moment. So since a "billion trillionth" is only 10^21, there are 5*10^9, or 5 billion, of those chances happening right now. – jamesqf Mar 27 '16 at 4:53
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    @Oddthinking : Agreed. I find it little difficult answering a question like this with proper references. I'll try to find a paper I was looking for last night. As for the calculation, it's trivial combinatorics - do I really need peer reviewed references for the equivalent of 1+1 = 2? (meta question, I guess...) – gilleain Mar 27 '16 at 9:37
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    I think your Talk.Origins reference has enough substance to use as the basis for your answer - quote their (referenced) calculations, and you are pretty much done! – Oddthinking Mar 27 '16 at 12:43
  • @gillean, this can be a good reference to add: ncbi.nlm.nih.gov/pmc/articles/PMC3543078 – nico Mar 28 '16 at 13:16
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Given the proposed mechanism of evolution (rather than the creationist parody of it) there has been plenty of time.

When Darwin was proposing his theory of evolution and long before the molecular basis of inheritance and biological structure were fully understood, he expressed concerns that the mechanism might struggle to explain some complex biological structures. He admitted that the idea that the eye, for example, could be formed by natural selection of small variations was absurd. How can a slow process selecting small improvements lead to something as complex and interdependent as the vertebrate eye?

Modern modelling of potential ways the eye could have evolved suggest that it isn't that hard. In a classic paper in Proceedings: Biological Sciences a model of how the evolution could have worked by the accumulation of small changes, each granting some advantage, suggests that complex structures can evolve quickly. Their model suggests that complex eyes could emerge from simple light-sensitive patches in less than a million years:

If selection constantly favours an increase in the amount of detectable spatial information, a light-sensitive patch will gradually turn into a focussed lens eye through continuous small improvements of design... Even with a consistently pessimistic approach the time required becomes amazingly short: only a few hundred thousand years.

The point here is that the intuition that a structure as complex as the eye could not arise by evolution is proved false by a good understanding of the actual mechanism involving the accumulation of small improvements. Simulation modelling using computer models has made this much easier to demonstrate.

Now that we understand the molecular basis of inheritance and biological structure creationist arguments tend to focus on the specific structure of proteins or DNA and make arguments based on the probability of randomly assembling current functional structures.

One of the first books to argue this point was Evolution: Possible or Impossible. For insulin the argument runs like this:

The Odds Against a Single Insulin Molecule

Before figuring for average size proteins, just for practice we may calculate the odds for the random alignment of the amino acid units for insulin, since insulin is usually considered the smallest protein, with 51 amino acids. Even insulin, it turns out, is not as simple as it first appears.

The insulin molecule is composed of two strands that must be linked together in an exact manner by sulfur bridges. To bring this about, the cell first constructs a longer chain of more than 80 amino acids called proinsulin. It ranges in length from around 81 to 86 in various animals. We will consider an insulin molecule of length 84 amino acids (of which an example is the pig). This extended sequence of 84 units causes the chain to fold and cross-bond correctly, and then a particular section of 33 units is cut out by special enzymes, leaving the final 51 amino acids in two chains properly oriented with cross links between them.

Chance will therefore need to align 84 amino acids in correct order to form proinsulin, as the precursor for insulin.

Since each of the 84 positions in the chain could be occupied by anyone of the 20 kinds, the total possible arrangements is 2084, which, after conversion to base 10, is roughly 10109. The different arrangements are considered equally probable; so the probability of anyone molecule being in the correct order for insulin is 1 in 10109. Allowing for one substitution (to be tolerated) makes it a bit easier for chance, and brings the probability down to 1 in 10106 approximately.

Going back to Dr. Eden’s statement that the total number of protein molecules that ever existed on earth might be 1052 as a liberal estimate, we will give chance another big boost by assuming that the 1052 are all different and are all the proper length for insulin. We can now figure the probability that any one of those would by chance be in correct order for insulin...

...Anyone of those 1052 is a different way that might fulfill the event of a chain being in the order for insulin. Therefore, the sum of the different ways is 1052. The probability that anyone of all that ever existed on earth would be insulin is therefore 1052 / 10106. Dividing in order to simplify the fraction, the probability is 1 in 1052.

Therefore, the odds are a million trillion trillion trillion trillion to one that not a single protein molecule of all that ever existed on earth would by chance be in the correct order for an insulin molecule! (Adjusting for different kinds of insulin would have little effect on a figure this size.)

But the core argument is deeply flawed when compared to actual mechanism proposed for evolution (as told in the model of how eyes might evolve). The creationist argument assumes that evolution has to randomly create a fully-functional modern structure and derived probabilities based on that assumption. But what the eye model demonstrates is that evolution can advance perfectly well by accumulating small changes that just add one small improvement at a time. It doesn't have to randomly create by shuffling a fully-functional modern structure.

Modern computers have made it much easier to see that this mechanism can be remarkably efficient. Algorithms for deriving good solutions to hard combinatorial problems by processes involving randomness and selection are remarkably efficient compared to alternatives (simulated annealing and genetic algorithms for example).

The other assumption that the creationist argument makes is that there are only a small number of 'viable' products (insulins in this case). They don't know this is true for two reasons. One is that modern technology has allowed the creation of a variety of non-natural insulins that work well in people (they are common in the treatment of diabetes); the other is that the original insulins may have had different functions or existed in different environments where they didn't have to be perfect, just better at whatever they did than their evolutionary predecessors. Again, comparison with the possible evolution of the eye suggests the creationist argument is simplistic.

Summary

Creationist arguments against the possibility of evolution make simplistic assumptions and are rebutted by a proper understanding of the proposed mechanism of evolution. Modelling shows that evolution can occur quickly even when generating complex modern structures. There has been plenty of time for evolution to happen.

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    "[Darwin] admitted that the idea that they eye, for example, could be formed by natural selection of small variations was absurd." This has been disputed as irony being used as a rhetorical device, e.g. by Dawkins. – Oddthinking Mar 27 '16 at 13:53
  • @Oddthinking A reasonable interpretation of what Darwin said, but not the only reasonable explanation. Maybe he was just being honest about reasonable objections he had not yet overcome. Neither matters for my argument, though. – matt_black Mar 27 '16 at 13:56
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    Darwin made that statement, and then with the next sentence began explaining how it could happen, so he clearly presented it as a possible objection which is readily overcome. – Mark Mar 27 '16 at 14:22
  • @mark and the modern simulation work demonstrates his intuition was right in a way that he could not making an even stronger demolition of the objection to his theory. – matt_black Mar 27 '16 at 14:24
  • @matt_black - agreed! – Mark Mar 27 '16 at 14:24

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