Saturday, 20 March 2010

Darwin was wrong.

This headline, or something like it, is a staple of lazy sensationalist journalists. It seems that every time something interesting about biology or evolution (I dont think there's a difference between the two but that's by the by) crops up in some study there's a semi-literate hack waiting in the wings to say that this proves Darwin wrong. Normally this just reflects a lack of understanding of the complexity of living things (which is of course evidence that evolution is true, no other mechanism can produce organic complexity). However sometimes it reflects a real lack of understanding of how science works.

We see the same bad reasoning whenever someone says something like “Einstein proved Newton wrong” or that “scientists are always changing their minds, one day they say one thing, the next they might say the opposite”. I think this reflects a real misunderstanding of the nature of the word wrong and does not reflect the historical reality of scientific progress. I dont think a scientific Theory is simply right or wrong as an absolute, nor do I think that future Theories are totally unpredictable.

I'm a mathematician and as such I think about everything as a mathematical analogy. To me science is a line of best fit. We are presented with data and observations. Given that we are required to predict what will happen in the future. All of science works like this, even history or other apparently non-predictive subjects work like this. When we say that there was a iron-aged fort at location X, we can interpret that as a prediction: “if more artefacts are uncovered from this site they will follow the distribution we expect from a fort of this size”. This is a prediction about future observations. Without future observations science is a meaningless task. Science is about constructing Theories, a scientific Theory is a (generally mathematical) model into which we can feed an experiment and from which we get a prediction. Any other sort of claim about the world is metaphysics, which bores me rigid so I wont talk about it.

So, given that, let us analyse what happened with gravity. Everyone knows things fall, the ancients said that the elements of earth and water tried to return to the ground and to the sea respectively. This is a scientific Theory. It makes predictions, and most of the time those predictions are pretty good. Rivers do flow towards the sea not away from it, rocks fall towards the earth not the sky. But then along came the Renaissance, then it was claimed that things fall towards the centre of the spherical earth at a constant rate of acceleration and that fire etc rise due to buoyancy. This is a very accurate prediction, it gives you much more detail than the ancient theory, if you've done any kind of mechanics with gravity in school, this is the theory you used. Newton then came along, and said that the force of gravity on earth was the same inverse square law that was known to rule celestial mechanics. This meant that very accurate predictions could be made for the force of gravity almost anywhere in the universe. And finally, Einstein shows up and yacked about bent space for a bit and allowed us to predict the precession of Mercury better than Newton.

What has happened here? I'm going to take some daft numbers for sake of example but they're not important. Let us say that the Ancient theory gives predictions that are as accurate as our instruments 50% of the time, this is very generous. Then let us suppose that the Renaissance model is as accurate as we want 90% of the time. What has happened to the ancient predictions? They're still just as valid. They're still easy to do and intuitive. They're still right with exactly the same accuracy. The Renaissance did not change the accuracy of the ancients. What it did do is provide a new theory that is more accurate. Anyone who stuck with the old theory ends up with worse results and is more likely to have things blow up in their face.

I claim that Einstein didn't prove Newton wrong. Before 1915 it was well known that Newton was accurate to within (made up figure) 1%, but it was also well know that this 1% error wasn't going away. Anyone who claimed that Newton's laws were perfect was either hopelessly optimistic or really out of touch with experimental results. After 1915 it was well known that Newton was accurate to within 1% and that whilst this is far from perfect it was used in the Apollo missions and almost all space-flight without too much worry. Einstein did not change this fact. One thing he did do that was important was knock down any notions that Newton was a god or had direct dealings with a god. This is very healthy. We need to remember that Einstein's Theory is more accurate than Newton's only quantitatively, it is accurate to within 0.1% not 1%. This is not the same thing as being right in an absolute sense. Relativity makes predictions about black holes and about the subatomic universe that just aren't right. All we say for Einstein is that these cases are rare so he's very accurate on average.

My point here is we need to get away from the notion that a Theory exists in one of two states, right or wrong. A simplistic version of the principle of falsification runs like this: we propose a Theory, provisionally accept it, then run tests, and if it fails them then it is wrong. I hate to disillusion you, but by that definition all Theories are equally wrong. Not one scientific Theory ever proposed has made 100% accurate predictions. Relativity goes all to hell near black holes, quantum theory is great, gets predictions right down to the 12th decimal place, but the 13th? Totally wrong.

As someone who's excited by physics I'm quite glad that a 100% accurate Theory Of Everything doesn't exist. A world where there was nothing left to do but measure some constants ever more accurately (as was thought by some at the start of the last century) would be a very boring one to live in.

Another suggestion that annoys me is that Theories change, so tomorrow a Theory may be discovered that is completely the opposite of the current one and that might be accepted. Remember the analogy of the line of best fit? I've got an extension of the idea. To me, Theories of science are a Taylor expansion of reality. A Taylor expansion is a sequence of curves of best fit that get closer and closer to the true value of some curve as time goes on.

Here we have a sequence of Theories, each one is an approximation of the real observation, each one is very close to right in a small area, and very far from right as you go away from there. I want to claim that these sequences of Theories have a very important property. As you go forward in time I want to claim that the numerical predictions made by a Theory will tend to get ever closer together before ending up very near some point.

I want to suggest that if you look at the history of mainstream Theories in one area of science you will see that over time the Theories become ever closer in predictions, until (as with current Quantum Theory) it is very very hard indeed to do an experiment where the difference between an old Theory and a new one is measurable. The red dots represent different Theories that are the most accurate available at different times. They fluctuate wildly at the start, then gradually settle down towards a definite value. What is that value? No way to tell, the best approximation we have is the most accurate Theory we have.

I suggest that if we observe one Theory to be very accurate then any more accurate future Theory will fall roughly within the error bar of the first. In short, I suggest that the green Theory could never be more reliable and accurate than the cluster of reds. Simply because if the green Theory is accurate you have a lot of work to do to explain why it is that all the red Theories work so well.

The Darwin example: Darwin wasn't a god. Of course he made predictions that have turned out to be false. And of course the core Theory of biology hasn't been left lying around for the last 150 years. We have new Theories of evolution all the time. Darwin's was simplistic, not very quantitative. It was an improvement on Lemark. It wasn't as accurate as the Neo-Darwinian synthesis. In the same way Richard Dawkins didn't show that evolution was wrong when he proposed his gene-centric version was more quantifiable and more accurate than group-selection theories. In the same way the latest improvement or refinement of the theory does not show that evolution isn't true. It is. Just now we have a better understanding of it.

It is of course always logically possible that anything could happen and any new theory could in principle be successful. But anything that seriously contradicts previous theories has an awful lot of explaining to do about why all the evidence of the past showed something different. I wouldn't dare suggest that it is impossible that evolution or some other well tested Theory will ever be replaced by a Theory that is substantially different. But it is a good prediction that this wont happen. I'm defiantly more confident than 1 in 2 million and would thus happily stake my life on it being true. (And so would you, you've taken a 1 in 2 million bet with your life if you've ever been on a plane for more than an hour).

Please note here I'm talking only about the predictive element of the theory. The metaphysical and philosophical differences between theories can be immense. The shift to a non-absolute time was enormous and totally contradicted all previous theories. But the change in predictions was very very small. The metaphysical difference between absolute time and relative time is vast, the predictive difference is billionths of seconds in any reasonable case.

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