In a comment a couple of days back in response to Petesquiz, I wrote:
If science were compared to a beautiful sandcastle, with towers and spires and turrets, statistics is the wave that sweeps over it and reduces it back to a low hummock of wet sand.
Many years ago, in the very first introductory lecture on probability and statistics, the tutor drew a rectangle on the blackboard, and several circles inside the rectangle, and invited students to imagine that the rectangle was a solid plane in which there were circular holes. He further invited us to imagine that there was a rain of particles falling on this plane, such that some landed on the plane, and some fell through the holes. Assuming an even distribution of particles across the plane, he then asked: “On average, what fraction of all the particles would fall through the holes?”
As one of the students in the lecture theatre, I was quite stunned by this question. And I had no idea what the answer might be. Or even if there was an answer. But the tutor went on to say that we knew that all the particles fell somewhere inside the rectangle, whose area R we also knew. And that we knew that the particles that fell through the holes landed only on the holes, and we knew the area C of these holes. Therefore on average C/R of the particles would fall through the holes, and this was also the probability that any particle would fall through a hole. How beautifully rational! This was the very first lesson in a long series of lessons, most of which I didn’t understand.
Now I think that, in retrospect, if I had not been so stunned, I might have raised my hand and said that his question assumed that we didn’t know the exact positions where all the particles landed. We only had a vague idea. And if we knew exactly, we would be able to give an exact answer to any question of this kind. So in one experiment with 10,000 particles scattered by hand over the rectangular plane, exactly 3,237 particles would fall through the holes, and in another experiment exactly 3,352 particles would fall through the holes. Nature always knows the exact answers to these questions: it is we humans who don’t know.
And therefore, in a profound sense, all probabilistic reasoning is reasoning that grows out of ignorance. It grows out of not knowing all the facts. It grows out of nescience.
And therefore any true and perfect science must necessarily be devoid of any kind of probabilistic reasoning of this kind. And any science which uses probabilistic arguments of this kind can be automatically described as a defective science. And the more that probabilistic arguments are used in any science, the more defective that science will be.
And since, to the best of my understanding, Quantum Physics employs statistical or probabilistic arguments throughout, we may dismiss Quantum Physics as a defective science (and perhaps the very best example of defective science). And in fact, since nobody understands quantum physics, the “success” of quantum physics has resulted in it becoming not so much a science as a nescience. It’s become a black hole in knowledge.
The “beautiful sandcastle” to which I was referring in my comment was the non-probabilistic science of Galileo and Kepler and Newton, which gave precise answers to questions: e.g. the semi-major axis of the Earth’s elliptical orbit has a length of 1.496× 108 km. But the arrival of probabilistic or statistical arguments was the arrival of a wave that reduced the beautiful sandcastle to a low hummock of wet sand. For with probability exactitude and precision vanish. Everything gets blurred. The length of the semi-major axis becomes iffy. It might be this, or it might be that. And if we add to that the fact that we are using mathematical calculators which might or might not be providing us with the exact right answers, then science – knowledge – must dissolve away completely into nescience.
And very arguably we are now witnessing the dissolution of the beautiful sandcastle of exact science into a low hummock of nescience. For it is now being argued that if there is even a 0.001% probability that Environmental Tobacco Smoke kills anybody in any year, then that means that in a population of 1 million people, ETS will cause the deaths of 10 people – which is utterly intolerable. Antismoking Tobacco Control zealots now conjure up hundreds of millions of dead people using statistical arguments of this kind. e.g. A Billion Lives. And these deaths are regarded as being as certain as the deaths recorded in drownings or traffic accidents.
People may object, like Roberto, that such arguments “can be easily refuted”, but it is unfortunately the case that they are not being refuted. They have instead become accepted common knowledge. They are repeated ad nauseam in the mainstream media. They are what Everybody Knows. Everybody knows that smoking causes lung cancer. When I lived in Devon I knew a woman whose father died of it. He hadn’t been a smoker, but he had once worked as a bartender in a smoky pub: post hoc ergo propter hoc. We have descended back into a medieval mindset in which anything, however improbable, can cause anything else.