Actually NO ONE has even insinuated that this scientists claim is an indication that the scientific method is flawed. I do maintain that her claim, AND the way some people try to brush it off as "not that big a deal" is a clear indication of the MISUSE of the scientific process, either intentional or not, in an attempt to use science to support a world view. VERY DIFFERENT from claiming that the scientific process is flawed.


The good thing is that in both Neo's post and the posts when we were trying to establish a common ground from which to base a discussion we are talking about probability.

Okay. If you really want to do this - lets start by getting the maths terminology straight.

For a start - in maths, the probability of an event happening is a number between 0 and 1. A coin flip would have a 0.5 probability of being Heads (1 divided by 2, as there are two equal possible outcomes), a single dice face would have a 0.166^. probability of being shown (1 divided by 6 as there are six equal possible outcomes) etc.

In maths, the way that probability works is that all possible outcomes for an event total 1. Not each outcome has to have an equal split, but they do all have to total to 1. An impossible outcome, such as flipping a coin and getting elbows, rather than heads or tails, has a probability of 0.

There is no such thing as a 1 in 10⁵⁰ Probability. As I've said, Probability is a number between 0 and 1. What I think you actually mean is there are 10⁵⁰ possible outcomes, which, if they're all equally likely of occurring, gives a Probability of 1 divided by 10⁵⁰ each.

If you stopped saying "Probability" and said "the number of possible outcomes" instead, I suspect everything will become much clearer.

An event having 10⁵⁰ or more possible outcomes is absolutely everyday and commonplace.

Odds of 1 in 10⁵⁰, however, are so long as to be considered impossible.

So - what's the difference between the two?

Quite simply, the odds are calculated by factoring the probability of an event happening with the number of times the event occurs.

Let's take Neo's example.



We have 999 red apples and 1 green apple, so, in effect we can say that we have a thousand possible outcomes, as any of these apples might survive. As we don't care which particular red apple survives, we'll group them into two possible outcomes - a red apple or a green apple.The probability of a red apple surviving is .999 [(1 / 1000) * 999], whereas the probability of our green apple surviving is .001 [(1 / 1000) * 1]

The odds for a red apple surviving a single barrel falling off the truck is 999 in 1000. The odds of a green apple surviving is 1 in a 1000. So far, this should make sense. The bit where people seem to come unstuck is when the event happens more than once.

Lets skip back to the old faithful coin example for a moment. We're going to flip it twice.

We know that for each coin flip, the probability of getting a head is 0.5, which has odds of 1 in 2. If we flip the coin twice - what are the odds that we'll get a head?

Let's examine all of the possible outcomes - there are only 4.

I could flip two heads, two tails, a head then a tail or a tail then a head. Those are the only possible outcomes.

Out of those 4 possible outcomes, only one of those doesn't have a heads - the two tails one.

This means there are 3 possible outcomes which do involve heads.

The probability of getting at least one head when we flip two coins is [(1/4) * 3] = 0.75, leaving 0.25 as the probability of no heads [(1/4) * 1]

The odds of there being at least one head when we flip two coins is 3 in 4. The odds of there being two tails is 1 in 4.

Fortunately, rather than write out all the permutations each time, there's a quick way of working out the new probability.

The probability of getting two tails in a row is the probability of getting a single tail multiplied by the probability of getting another single tail, i.e 0.5 * 0.5 = 0.25, which has odds of 1 in 4 of happening.

Skipping back to the Apple example, we can see that if the event happens twice, then the probability of the green apple surviving twice is 0.001 * 0.001 = 0.000001 or odds of 1 in a Million.

Do it three times and we get 0.001 * 0.001 * 0.001 = 0.000000001 which has odds of 1 in a thousand million.

This is why scientists can be reasonably sure with a limited number of samples that are the same, that they're looking at the rule and not the exception to the rule.

In this particular case, I'd personally be a lot happier if we could validate the result with a number of other teeth, because, as I've illustrated, it would significantly strengthen the case that they were looking at a common event. In short, I'd be wary of calling something with a 1 in a 1000 chance of being wrong a fact, whereas I'd certainly feel more comfortable if it was at least a 1 in a thousand million chance or above.

Tiggs, maybe we can start another thread to discuss probability and chance because it is a very interesting topic. I apologize for derailing the discussion by bringing up an issue from another thread.

The thing is, the red apple/green apple analogy is oversimplifying the question and in doing so, does a disservice to anyone and everyone truly interested in learning something. Assuming that the ONLY meaningful variable is the population size of normal Neanderthals compared to the population size of abnormal Neanderthals in determining whether a fossil comes from a normal Neanderthal or not is incredibly simplistic. For one, it doesn't take into account that certain geographic/environmental locations are more conducive to fossilization than others, or that predation and scavenging also have an impact on fossilization. If our abnormal Neanderthal happened to die in an area with no scavengers which also happened to have the correct type of geographic/environmental conditions while the normal population did not, then the probability of finding a fossil from a normal Neanderthal drop to almost nil, while those for finding the fossil of an abnormal Neanderthal increase dramatically. So, there are a great deal of variables we have no way of determining which are at least as important as the size of a population before we can say one type is more likely to be fossilized than another.