Creation & EvolutionForum for the discussion of this important topic. This forum is open to non-believers. There is a Christians-only forum in the Christians-only section too.
I've been reading the forums for a while, and it amazes me that so few people understand basic probability, and yet they continue to use it in an attempt to disprove evolution. I decided to write this post to explain why the argument that evolution is impossible and improbable is a bad argument and hopefully clear up some misconceptions. I tried to keep it math-light, and if you have any questions, or if you spot any mistakes, please let me know. I'm on summer break now, so my brain is officially mush until next semester.
This argument only address the fallacy of evolution being impossible because it only has 10^-100000000000 chance of occurring according to some random guy (not me).
Basic Probability Information:
Suppose we are rolling a dice and we are interested in what number is rolled. This is called an experiment. We will not be able to predict the outcome of this experiment, but we do know all the possible outcomes. The set of all possible outcomes is called the sample space (S). For this experiment, S = {1,2,3,4,5,6}. Any subset of the S is called an event (E).
A probability of an event (or P(E)) must follow three conditions.
(i) 0 <= P(E) <= 1 (there is a 0 to 100% chance of something occurring)
(ii) P(S) = 1 (there is 100% chance of something in the sample space occurring)
(iii) Probability of the union of mutually exclusive events is equal to the sum of the probability of each event. (Example: P(1 or 4) = P(1) + P(4))
To determine the probability of an event, if all events are equally likely, the basic formula for P(E) = size(E)/size(S). Basically, how many ways can event E occur divided by the size of the sample space.
In our example, if we want to determine the probability of rolling a 4 on a fair dice, we take the number of ways to roll a four (1) and divide it by the sample space (6) P(4) = 1/6.
E can also be more than one outcome. Let's find the probability of rolling a number between 2-4, E=[2,4]. Remember that (iii) states you can add the probabilities of the individual events. P(E) = P(2) + P(3) + P(4) = 3/6.
More Probability Information:
Our example of rolling a dice is a discrete example. The sample space is countable. We'll now move to the continuous example. All the rules of i-iii still apply.
To determine the probability of an event in a continuous sample space, you need a probability density function (pdf). While this sounds scary, it's just a function, f(x), that represents the probability of something occurring. Here's an example of a pdf.
For example, let's find the probability of E=(.5 < x < .6). Remember in the discrete case, we just summed up all the values between 2 and 4? Well, the same basic idea applies here. However, there's an infinite amount of points between a and b!
Well, this is where calculus comes to the rescue. The probability of an event is defined as the area underneath the pdf of that event. As you forgot, to find the area underneath a curve, you take the integral of the function of the curve between your points.
Our experiment will now be the arrival time of a bus. Let's assume the bus always arrives between 1:00 and 2:00 and it has equal probability to arrive at any time inbetween. Our sample space is [0 hour, 1 hour]. This means the bus can arrive right away, any time before an hour, or at the very end of the hour.
The line is our PDF. It's basically
f(x) = 1, 0<x<1.
f(x) = 0, else where.
(more on next post....)
EDIT: fixed images
Last edited by random_guy; 22nd May 2005 at 07:58 PM.
If we want to find the probability that the bus arrives between 1:15-1:30 (E=[.25-.50]), the probability would look like this:
The probability of the bus arriving between those two times is 25%.
The Impossibility of the Bus:
Suppose that we're running late, and we rush to the bus station. Right when we arrive, the bus arrives. Let's let the time be 1:45. What's the probability of this event occurring?
Uh oh. What just happened? There's 0% chance of the bus arriving at 1:45? What about the chance of the bus arriving at 1:46? 0%. 1:12? 0%. When you see that bus arrive, it had a 0% chance of arriving at this time. How is this possible?
Does God intervene to make the bus beat all odds and show up? There's better odds of me turning into an atheist, becoming President, while dating Natalie Portman than there are of that bus showing up at that time.
What's going on here?
Flaws of the Bus:
The problem with entire bus probability is that there's an infinite number of possible times that the bus can show up. The odds of it landing on that exact one is technically impossible. However, the bus has to arrive at some time. If you want to find a probability of any value, you must examine a set from that sample space. For example, if I asked, what's the probability that the bus shows up between 1:15 and 1:15 and 1 second, then I would get a valid answer (~.003%).
Flaws of the Impossibility Argument:
Now, you might counter that the impossibility argument doesn't have an infinite solution set, it's countable. However, the same flaws apply. There are a huge number of outcomes in the sample space, but the argument is asking the probability that an exact one occurred. Of course that number is going to be small. However, the argument doesn't examine what other similar outcomes can occur if the event is changed by a bit.
After that outcome did occur, did it really beat all odds? Or was it like the bus example, where something has to occur. Remember, a bus has 0% chance of ever showing up at a specific time, but the bus will eventually show up. Just like an argument of a specific protein being impossible to form required for some specific advantage, perhaps some protein will show up giving some advantage, it just happened to be this certain protein that did.
Conclusion:
Before you argue that something is impossible, remember to stop and think about three things:
1) What is the sample space? If it is large, the probability of a specific event will be small.
2) What is the event? If the event is a specific event, the probability will be very small. Are there other events
that can lead to the same outcome? Are there other events that can lead to similar outcomes? Have you even thought about other events?
3) What are the possible outcomes? If you are focusing on one specific outcome, the probability will be very small. Have you considered other outcomes?
Take this things in mind before you argue about probability. Again, this post did not mention other flaws with the impossibility argument such as non-uniform probability, errors in determining that probabilities, etc. If you have any questions, please feel free to post it.
EDIT: fixed pictures
Last edited by random_guy; 22nd May 2005 at 08:00 PM.
*You must spread some Reputation around before giving it to random_guy again.*
__________________ And since they could not bear the truth, these singers, who might in some other place have been wise, were squeezed under the terrible weight of the warren's secret until they gulped out a fine folly--about dignity and acquiescence and anything else that could make believe that the rabbit loved the shining wire. But one strict rule they had; oh yes, the strictest. No one must ever ask where another rabbit was and anyone who asked 'Where?'--except in a song or a poem--must be silenced.
And of course no one who needs to read the thread will.
__________________ "If we begin with certainties, we shall end in doubts; if we begin with doubts, and are patient, we shall end in certainties."
-Marcus Aurelius
Knowledge3 you might have missed the point to this....
FANTASTIC THREAD!!!!!!!! How come it is not in the quiet thread yet?
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