Wednesday, 19 March 2008

Probability (and how to use it)

It seems that a lot of people like to throw around probability when arguing, though it's even more apparent that most of these people don't know how to do it. It does help having a solid knowledge of mathematics but it really isn't necessary. It's not hard to know the difference between a single event and a chain reaction.

Evidence-based approach
It should be made clear right off the bat that science doesn't work on probability alone (with the exception of quantum physics). It works on evidence.

If I pick my iPod off my desk and leg go of it, what will happen?
There are three options:
* It will fall to the ground
* It will stay where it is
* It will move away from the ground
Using probability there is a 1 in 3 chance of each one happening

So that's it, a one in three chance? Well no. Since my iPod is a piece of junk (seriously, don't buy iPods) I don't mind conducting this experiment. I let go of it a total of 20 times, if it were just pure chance as people suggest probability is, I would see a even distribution on the three options.

The results were:
* fall to the ground - 20 times
* stay where it is - 0 times
* move away from the ground - 0 times

So what this shows us is probability isn't simply working out the possible outcomes and assigning an equal weighting to it. Probability should always be tied to evidence. And the more times we do a test, the more we can see it working. Repeatability is an immensely important factor in the scientific process. From observation and repeatability we can derive theories, formulas to explain the results and it allows us to test those theories under multiple conditions. I don't think anyone would dispute gravity as being anything other than a law, yet it's not proven. Gravity is a theory, just like evolution is. You can never prove science by example, only disprove it.

This is great news, it gives us relative certainty in an uncertain universe. It means that if you jump off a building you will fall. And using laws derived from observation, you will accelerate until you hit an object that will push back harder on you than you will on it. And it will almost certainly kill you as observable evidence shows that the human body can't absorb forces of that magnitude.

Evidence is the fact we have to work with in science, with evidence we look for an explanation to make sense of it. They don't call an idea a theory until it is quite rigorously scrutinised with suitable evidence to support it.

Coin flip logic
To understand the difference between combination and chance, let's look at a simple test of flipping coins. They have a 50/50 chance where it can either be heads or tails. Makes for a useful tool in seeing how to analyse a repeatable task statistically, and how to understand how combinations work.

Flips - 10
H - 6

T - 4
After 10 flips, heads is more common. This is were repeatability comes into it. Let's go on.

Flips - 10
H - 3
T - 7
Cumulative total: H - 9
T - 11
Now there are more tails, but we can see it's getting closer to that 50%. Of course the experiment is biased by the way I flip the coin, there is no way to make this truly random. But we can see that it's getting closer to that 50% chance mark. One more time for good measure

Flips - 10
H - 7

T - 3
Cumulative total: H - 16 T - 14
The more you do something that has an certain probability, you can see that probability manifest in statistics. Rolling a die is another way to do this, rolling enough times should yield you statistics that show approximately a 1 in 6 chance for each possible result. With a deck of cards, a 1 in 52 chance, though you'd need to do it a lot of times to see that manifesting. The more variables, the more testing is needed to see accurate statistical significance.

The most interesting pattern is the sequence is the patterns involved. In the last throw sequence there was 5 heads in a row. The probability for that to happen is 1 in 32 (1/2 * 1/2 * 1/2 * 1/2 * 1/2). So on throw 5, what was the chance of me throwing a heads? It was still one in two. Patterns themselves are improbable, but the steps that make up the patterns are not. Which brings me to evolution.

Evolution and God
Evolution has overwhelming evidence to support it, it's been observed, there are extensive fossil records, the DNA evidence, genetics, the list goes on. Yet people still talk about the probability of evolution. How could we be an ancestor to modern prime-apes one day then humans the next? That would be highly statistically unlikely. But we didn't go in one step, we went in thousands of small steps. Take the average age of reproduction as 25 (a very conservative estimate) and there would be ~240,000 generations between our great ape ancestor 6 million years ago and us. 240,000 generations of environmentally caused mutations, diverging species (most of which died out), and suddenly the steps are a lot smaller. We don't have to lose all fur, walk upright, grow a bigger brain and develop complex vocal chords all in one hit. we can do it in small stages.

And the evidence points to this, through fossil records we can see a gradual change over hundreds of thousands of years. Even now we are still evolving as a species, there are mutations we can see in descendants of certain areas that aren't there in others. What we can do with probability is work out the rate of mutation and see if that is realistic over a 6 million year time frame. In one jump, I agree it's very unlikely. But evolution does not work in huge leaps. Evolution is a very gradual process, so the likelihood of slight mutations at each step is far more likely.

Moving on to God, a lot of people make the fallacy that God's existence is the probability equivalent to a coin flip, he either exists or he doesn't. Now when I say God, I am talking about the anthropomorphic deity that is the centre of Judaism, Christianity, and Islam. In this context We are told that God is a vastly complex deity, one of infinite intelligence and power, one who is all loving and concerns itself with the melodramatic squabbles of the human race. Now there are two things that come out of the creation story that don't add up; the first is how a being such as God came to exist, and how life formed out of nothing. If the being called God can be explained, then the 2nd event seems somewhat rational with logic, if there is a being with the power to create a universe, surely it would follow it could make humans from dirt.

As I explained above, when it comes to probability, it's always about it's intrinsic link to evidence. God is not 50/50 any more than the existence of Zeus. In the case of scientific enquiry, it takes a sceptical approach and asks for evidence. And at present there is no evidence that God exists any more than Bigfoot, The Loch Ness Monster or Albus Dumbledore. The best we can do is look at the world around us and use a critical eye on the evidence to see how much of a logical leap that is. As Carl Sagan said: "Extraordinary claims require extraordinary evidence"

It's all to do with plausibility. If I were to say I'm levitating as I type this, no-one would believe me. They would call me a liar, ask me for evidence. And that is perfectly reasonable, it's an extraordinary claim that I'm doing something out of the bounds of human reality. Would anyone here take it on faith or say there is a 50/50 chance of it being true? I really hope not. A picture could show me levitating, but pictures can be taken mid-jump or doctored on photoshop. A video would be more conclusive, but again they can be edited easily on a basic computer or I could be concealing my levitation by a concealed trick. We need to understand that probability is absolutely useless without evidence and context.

The principle of parsimony
Don't get me wrong, probability is a powerful tool when used correctly. But it's abused time and time again by people who don't seem to understand how to use it. We see Pascal's Wager come up again and again. We see bile like The Probability Of God littering our shelves. Absurd claims that evolution and abiogenesis are improbable. All these sound good, but they aren't using probability properly. It seems as dangerous a practice as quote-mining for anything that can vaguely sound theistic in scientific journals. It's not that hard to understand how parts come together. Science is all about breaking down the how and finding how each little part works. If we can explain the pieces and can explain how the pieces can come together it makes it a far smaller assumption than just seeing the whole and thinking it came together in one big step. We apply the principle of parsimony because it gives us the most accurate representation we can possibly get. Probability plays it's part but only when used properly.

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