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OK, let's review. We have learned three things here:
Keep all of those facts in mind when examining any creationist probability argument, because they almost always ignore all of them. In fact, now that you are armed with a basic comprehension of the difficulties inherent in probability calculation, you should be able to see through the following common creationist tricks:
Creationist probability calculations are usually characterized by their extreme simplicity, as if there's really nothing more to probability than counting the numbers of entities involved in a process and turning them into an exponential figure, with no regard whatsoever for whether the process is characterized by many valid picks or only one. For example, in poker, the odds of drawing a royal flush are very low, but the odds of drawing a double are very high, because there are so many doubles. When creationists speak of the odds of evolution or abiogenesis, how do they know they are looking for a royal flush or a double? How do they know how many valid outcomes exist? Quite tellingly, they never even mention this question, because it's so much easier to assume that there is only one.
They also ignore the question of whether events in a series should be treated as separate events or a single combined event. And yet, as we saw in our "rolling dice" example, this is an enormously important factor. If 500 binary events are required for something, a typical creationist would literally assume that you can compute the odds of this event by simply punching "2^500" into a calculator, with no regard whatsoever for the underlying mechanisms or the manner in which these events should be combined.
We have already seen that there is a huge difference between random probabilities and non-random probabilities. Unfortunately, most creationists falsely assume that all natural processes are random, which is why they usually describe evolution as "random chance". And yet, we saw with the case of modified poker that the addition of as little as one rule can completely falsify random probability calculations! If this is the case, then how much effect do all the myriad rules of organic chemistry have? How can anyone seriously call organic chemical reactions "random chance" when they have so many rules that most people struggle to grasp the few rules they describe in high-school chemistry?
The assumption of randomness is so deeply buried into creationist thought that almost no creationists even state it as an assumption; they simply incorporate it silently into all of their arguments and hope that you won't even think to ask the question.
Once we realize that we are dealing with non-random processes, we run into a serious problem: as we saw in our modified poker example, it would be impossible to calculate the odds of drawing a royal flush if you don't account for the modified draw rule, and it is impossible to account for the modified draw rule if you don't know what it is. In a situation like this, you cannot compute probabilities no matter how much of a skilled mathematician you are.
Now that you (hopefully) understand how difficult it is to generate probability estimates even for a situation where you know most of the variables and mechanisms, how can you generate such precise estimates for events where you don't know so many of the variables? And why does the math behind these creationist probability estimates look so nice and clean and simple?
Are your suspicions raised yet? They should be. You've seen how complicated a probability analysis can be for something as simple as a game of poker. How can creationists possibly derive such mathematically simple probability estimates for something as remarkable as the origins and development of biological life? Sure, you could say that their stratospherically high probability estimates are perfectly reasonable for something you find so alien, but that's not much of an answer, is it? Probability estimates are most accurate when you know the situation very well, not when you don't know it at all. The sheer simplicity of their work is proof of its inaccuracy: the idea that complex catalyzed organic chemical reactions could be modeled in such a manner that they are far simpler than a mere poker game is the height of absurdity, yet it is widely accepted practice in the creationist world.
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