Rolls, when I see such offhand rejection of science based simply on rough conjecture, and often borne out of wishful thinking (and hey, do we not all wish that big and complicated problems like AGW were not real and would just go away?), it makes me a sad panda.

When we can accurately predict the weather for tomorrow, ill listen to the guy who says the sky is falling
This is a common sentiment. But it is based on a flawed understanding of the nature of prediction and probability. Can we predict the weather for tomorrow to the degree that we know what the exact temperature will be at midday, how much rain will fall, how many hours of sunlight etc etc? No, not accurately or to a high degree of certainty. Can we make a rough prediction based on our limited knowledge? Yes, and we can also give a percentage likelihood that the prediction will come out.
But even if short term prediction is inaccurate, that does not mean long term predictions about underlying trends are harder. An example from maths: random numbers. If you have a (perfect) 10-sided die, numbered 0-9, and roll it over and over, recording the results there are two things that are true:
1) You have a very low chance of correctly predicting the result of the next roll.
2) The more times you roll, the more likely that any particular number will come up 1/10 of the time.
So, for one roll, I could say it will be a 7, but I will very likely (90%) be wrong.
For ten rolls, I could say that 7 will come up at least once, and I will likely (65%) be right. The chances that it is exactly one time are still pretty low (about 30-40%?)
For a hundred rolls, I could say that 7 will come up 10 times, plus or minus 2 and I will likely be right. I'm not sure of the exact probability, but we are approaching 90-95%
For a thousand or a million or more? By the Strong Law of Large Numbers, the result will tend to be that each digit will occur 1/10 of the time. The probability of making an accurate prediction will tend towards 100% as we tend towards rolling an infinite number of times.
What’s more, if you look at your records and look at every pair of digits, you will get a string of numbers between 0 and 99. Again, the longer you keep going, the more the results will show that any particular two-digit number will appear 1/100 of the time.
Now, if that phenomenon can be seen in something
totally random it can also be observed in a system which is very complex but has underlying patterns. Thus, just because we cannot predict the weather for tomorrow (which is specific, not general) as accurately as you may want does not mean that we cannot make longer term predictions about the climatic trends (which are general, not specific).
Don’t believe me? Let us look at some variations and increase the complexity as we go.
First, consider a loaded die. It is biased towards the number 7, so that it will come up more often. Say… twice as much.
If we repeat the same sequence, the chance of getting any one roll correct are still low – not as low, but 20% is not very accurate as a prediction. However, similar to before, the longer we keep rolling, the more likely it will be that 7 comes up exactly 2/10 of the time.
Secondly, consider a die that we think is loaded, but have no idea whether it is or not, or by how much.
At first, we have no way to predict what any particular roll will be, or even be sure what the chances are of rolling a 7
If we run through a large number of rolls, we will end up with a series of results giving a frequency for each number. The longer we do this for, the more likely it is that we will then find out how loaded the die is and get a probability for each number coming up.
Then, we can use that to say what the chances are of a particular number (or member of a set of numbers) being rolled in any individual die roll.
We still cannot predict the next number, but we know a lot more about the die than when we started.
Now, let us go even further, and consider a dice making factory. It makes hundreds of them a day. It tests a sample of them at regular intervals to see if they are true or loaded. All kinds of factors can affect whether a die is loaded – wear and tear on the machines, quality of the raw material, prevailing pressure and temperatures, the way people handle the machines, the design and manufacture the plant, and so on and so on. But also, there is a random factor that can’t be accounted for and a basic minimum proportion of dice will always be loaded. The managers notice that the frequency of loaded dice varies over time but seems to be more than it used to be. What do they do?
Well, if I were the owner and wanted to have the lowest number of rejects I would expect that they would try to work out what the conditions were when more loaded dice were produced to see if they can detect any correlations. Then I would like to see them testing those correlations to see if they are consistent or not. Also, to look at the theory of what they are doing to see if there are some factors more likely to be in play than others. They should try to work out which ones are having an effect and come up with possible ways to reduce the risk of producing a duff die. It may be that they conclude that the problem is mainly down to ageing plant, or an under-skilled workforce, and that the remedy would involve me spending capital or revenue in order to reverse the trend. Maybe I do not want to do that. If I balance out the risks and costs and decide based on the best information to hand how to proceed, that is rational.
If I challenge their conclusions on the basis of their results, or look for alternative explanations, or even if I challenge their data collection methods, at least I am engaging with them in a rational way.
If, however, I say that I will ignore them until they can more accurately predict the single roll of a die, then I am being an, umm, IDIOT, to use your own word.
By sheer coincidence, I was listening to a programme about randomness and pseudo-randomness on the radio this morning, before I saw your post. The counter-intuitive nature of what comes out of fairly straightforward maths is mind-boggling. Part of the problem is actually in how our minds work, which just adds to the boggle-factor. We can make patterns out of chaos, but we also suffer from cognitive dissonance which means we see patterns where there are none (or no pattern where there is one). This is where the tool of science comes in handy, as it sorts the wheat from the chaff. No wonder that what we would think of as common sense seems to be at odds with what science tells us, though, because often it will give us a result that our brain is not expecting.
A long post, but now my inner panda has his bamboo shoots
