A point about probability

The thing about math is that we get to wave our hands for a much shorter time than in some other disciplines. In very short order, we are called upon to sit down and do the math.To start with, in order to realize the stated goal of using probability to disprove evolution by natural selection, it would be necessary both to learn probability and to have an actual and accurate probability model for evolution by natural selection. The first point is relatively easy and the second point is absolutely crucial.First, what's the probability of two things both happening if we know the probability of each of them? For example, given the probabilities of p₁ and p₂, probability p of them both occurring is:

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p = p₁ p₂

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Since all probabilities range from 0 to 1, inclusive, if p₁ and p₂ are both less than 1, then p is less than either of them.Another example would be the flipping of a coin and getting heads (which we will assume is 0.5, even though that's a bit off due to the uneven distribution of mass in a coin). If we flip the coin twice, the probability of heads both times is (0.5)² = 0.25. If we flip it 10 times, then the probability becomes (0.5)¹⁰ = 0.0009765625. And so on.That coin-toss example has often been used in the past by creationists to "disprove" evolution. An obvious problem with it is that it falsely assumes that a fixed sequence of events must occur one after the other, for generation after generation, without any breaks. Rather, there can be breaks in such a sequence that last for several generations without disrupting such a sequence in the least. Also, we're not just dealing with an individual line of descent, but rather with an entire population of individuals. So the question becomes: within a given population, what is the probability that at least one individual will acquire the mutation?That is a different kind of question. We already know how to calculate the probability of p₁ and p₂ and p₃ and p₄. But now we need to calculate the probability of p₁ or p₂ or p₃ or p₄. Here is my approach:In order to find the probability of something happening at least once in a given number of attempts, we figure out the probability of it not happening.For any probability p of something happening, there is a probability q of it not happening, such that:

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q = 1 - p
which also says that
p = 1 - q
which we will use later

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So if we have a probability p and we want to know the probability of it happening at least once in n attempts (P), that would be:

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q = 1 - p
Q = qⁿ
P = 1 - Q = 1 - qⁿ

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To keep the first test simple so that we could do it by hand, let's do the coin toss again. p = 1/2 and n = 4. What's the probability of heads coming up at least once?

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q = 1 - p = 1/2
Q = qⁿ = (1/2)⁴ = 1/16
P = 1 - Q = 1 - 1/16 = 15/16

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OK, now lets take a simple evolutionary situation, plug some token values in, and see what answer grinds out. The ony difference here is that we will need a calculator, so I'm using Excel so expect some round-off in the display.Two mutations. Let's given them an equal probability of happening -- oh, say, one in a million. We have a population of 100,000. What's the probability of those two mutations both showing up at the same time in at least one individual within 100 generations?

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p = (10^-6)² = 10^-12
q = 1 - p = 0.99999999999900
Q = q^{100,000 100} = q^10,000,000 = 0.99999000027
P = 1 - Q = 9.99973 10^-6
or about 1 in 100,000

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Not too probable, but nowhere near "astronomical".Of course, we had over-restricted that into an unrealistic scenario. That scenario required that both mutations appear at the same time in the same individual, but there's no reason to place that requirement. The usual scenario is for one mutation to be neutral and then selection starts acting on it when the second one appears. In that case, then what's the probability of one of those mutations appearing?

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p = 10^-6
q = 1 - p = 0.99999900000000
Q = q^{100,000 100} = q^10,000,000 = 0.0000454
P = 1 - Q = 0.9999546
or just a smidge less than dead certainty

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Within 10 generations, P is 0.63212. Within one generation, it's 0.095. Yet again, hardly astronomical.Of course, to come up with meaningful results, we must have an accurate probability model for evolution as well as the actual probabilities of the events happening. Rather, the purpose of this exercise was to demonstrate the effects of populations and multiple generations on any probability calculations.And when creationists present their probability arguments, then their probability models must be examined for accuracy. And above all, we cannot simply accept their conclusions supported solely by hand-waving. We must insist that they do the math and that they show their work!PS
Case in point: Kent Hovind made a claim that, since the sun "burns its fuel" at a rate of 5 million tons per second, that means that 5 billion years ago the sun would have been so massive that it would have sucked the earth in from its orbit. Sounds impressive. Astronomical numbers and lots of creationist hand-waving.But if we do the math, we will find that the total mass lost at that rate over a period of 5 billion years only amounts to a few hundredths of one percent of the sun's total mass. IOW, a fairly insignificant loss that would have only affected the earth's orbit by about 600,000 of its 93 million mile radius.Just another object lesson to do the math!Edited by dwise1, : PS

You missed the point. The only way that the scientific community would take any notice of statements regarding probability would be only if they were based solidly on a valid mathematical model. A valid probability model and valid values for the probabilities being used.So far, the creationist community has not presented any valid probability model, but rather nothing more than BS. Claiming that evolution is like tossing a coin a million times in a row and come up heads each time (which I have seen them claim) is pure BS. Claiming that evolution is like a tornado in a junkyard assembling a 747 is pure BS. Claiming that a modern protein would have had to have come together in a single trial is pure BS. All creationist probability claims are good for is to deceive themselves and their audience.That is why, if you are going to have any hope of using probability to argue against evolution, you will need to use a valid probability model for evolution, along with valid values for the probabilities involved. That was the main point I was presenting.In order for you to do that, you will need to study evolution and learn as much about it as you possibly can. Rather than to requote Sun Tzu yet again, if you don't know your enemy nor yourself (and most creationists are abysmally ignorant of both), then you will have no hope of winning this fight. The only way you're going to have any credibility is if you have done your studying and you know what you're talking about. So far in nearly 30 years, I have yet to see a creationist who knew what he was talking about with regard to evolution or to other pertinent scientific subjects -- judging by their arguments; it's possible that some knew some science, but they were too willing to lie about it for that knowledge to come through.The model that I presented is inadequate for the job you've laid before yourself. However, it illustrates the effects of a factor that you will need to incorporate into any valid model of evolution: populations. In fact, you might want to start out by looking into population genetics. One scientist described natural selection as being able to make the improbable inevitable.You will also need to be very clear on what you mean by "mutation" -- in evolution, that refers primarily to genetic mutation, changes in the DNA, rather than to gross corporeal changes which most creationist references to "mutation" mean.I noticed earlier that you described evolution as "chance". It is not, though it is stochastic. That is to say, there are so many factors involved that we cannot work it all out, but we can observe the outcomes and from those observations work out the probabilities of what outcomes to expect.I've seen some attempts to reconcile the idea of miracles and the Laws of Nature. Some have tried to argue that God had inserted exceptions in those Laws in order allow the miracles He had already planned out. The best that I heard is that miracles are outcomes that are very highly improbable, virtually impossible, but not completely impossible (ie, p=0 is impossible, whereas p approaching zero is still possible, but so highly improbable as to be deemed virtually impossible). So a miracle is God letting the virtually impossible happen.You cannot believe that God could have formed Man through evolution? You don't think He's capable of guiding the process? So He's not so omnipotent after all?I've usually found that when our understanding of the world is at odds with how the world really is, then the problem must lie in our understanding of the world.

So you're telling us that you believe that your god is powerless in the face of Nature?Well, that's certainly true of the god of creationists, which is better known as the "God of the Gaps", who can only exist within the gaps of our knowledge; that god gets diminished every time we discover a natural explanation of something. Rather, what I've heard from non-creationist Christians is that their God is "Sovereign over Nature" and as such is immune from the discoveries of science. Science presents constant danger to the "God of the Gaps", which is the creationists' chosen god, but it presents no danger at all to the "Sovereign over Nature".Again, you had missed the point. Theology is the study of God. It is a fallible human attempt by fallible humans to understand the Infinite. It is very imperfect. Furthermore, nobody follows a specific theology that is taught them, but rather everybody creates his own theology based on his incomplete and imperfect understanding and on his misunderstanding of that and other theologies.So, when one's theology demands that the world must be a particular way or else God does not exist, and the world fails to conform to those demands, then what's the more likely conclusion to be reached? That God does not exist, as his theology demands? Or that his theology is incorrect in those demands that it had placed on the world and what the world must be like?And when he comes to realize that his theology is incorrect, then what? Since it was incorrect in those things that he could check, does he then continue to believe it and follow it's command that he stop believing in God? Or does he figure out that he cannot believe that part of it either?

Not when they are doing science, because science cannot work with the supernatural. We have no way to measure, observe, detect, or even determine the existence of the supernatural, therefore we have no way to test any hypothesis which is based on supernatural forces or on the intervention of supernatural entities. The supernatural simply has no place in science because science cannot work with it.That does mean that science requires everyone to renounce personal belief in the supernatural, contrary to what IDists falsely claim. Science only requires that supernaturalistic hypothesis not be used in scientific work. Therefore, a scientist can very well work with natural selection while at the same time independently holding a personal belief that his god might have nudged it at the right times to bring about the world that we see before us.My point was that, since your theology should have taught you that God had created the universe, along with the Laws of Nature, that the fact that the world runs in accordance with those very Laws does not necessarily leave God out of it. For decades I have seen creationists claim that if evolution is true, then God does not exist. And for decades I have seen former creationists become atheists when they discover that their creationism is indeed wrong, just as their creationism had taught them to do.But when that happens, it's not science and evolution that had turned them into atheists, but rather it was their own theology that had demanded their deconversion. Therefore, the question to ask is not whether science and evolution necessitate atheism, but rather whether those creationist theologies are correct in requiring atheism.BTW, the probabilities you have been raising have nothing to do with natural selection, nor is natural selection driven by mutation. You need to study more and to learn what evolution is and how evolutionary theory says it works. Until you have learned how evolution works, you will be unable to devise a mathematical model that can even begin to describe it.Here's an extremely rough and incomplete outline:
1. A population exists. That population's gene pool (the genomes of all its members) contains a degree of variability; ie, its members are not genetically identical to each other. This is genetic variability.2. Members of the population go about their daily business of trying to survive. They may or may not be aided (nurtured) by their parents or other kin. In general, those who are better able to survive will have a better probability of surviving to the point where they can reproduce. This is natural selection; it acts to lessen genetic variability.3. The population reproduces. This creates offspring who are very similar to their parents, the survivors, and so they generally possess those traits that had helped their parents to survive. Yet they are also slightly different from their parents, so some may not have all the survival traits of their parents while some may have slightly better survival traits. This is reproduction, which also helps to increase genetic variability.The probability "problem" you pose only deals with increasing genetic variability, not with natural selection. Any viable probability model you devise for evolution will need to deal with both aspects. Actually, what I've been advising is that the only hope you could possibly have of succeeding in your endeavor is if you were to do what no other creationist has ever done: devise a valid model that does accurately model evolution and do the math.However, I am quite sure that such a model will demonstrate to you that probability does not provide any argument against evolution. That is why I had tried to prepare you to examine your reasons for trying to disprove evolution in the first place, that being your theology. No, probability works for any number of trials. It is for the larger numbers of trials that we should see the anticipated probability distributions appear. And since the probability distributions of their games do favor the house -- however slightly in some cases -- , that is indeed how casinos make a living. It is in the smaller numbers of trials that one might be able to "beat the odds", but in the long run the house always wins.The thing with using probability to model evolution is that we need to do so accurately. Which involves populations and generations.Gotta run now.Edited by dwise1, : No reason given.