I came across a sentence in an article I was reading:
“statistics are… just cold hard facts.”
I disagreed immediately. I don’t think statistics are “cold hard facts”. I think they’re fuzzy facts. Or even elastic facts that can be stretched to cover almost every eventuality.
Hard facts are surely facts that firmly say Yes or No. But with statistics it’s always Maybe. If you have a one-in-ten chance of getting some disease, then maybe you’ll get it and maybe you won’t. It could be true that you get the disease, or it could be untrue. True and untrue can co-exist in statistics, and can swap places. It’s perfectly legitimate to believe that you won’t get the disease, and it’s perfectly legitimate to believe that you will. And one result of that is that no debate can ever be resolved. Everything is always possible. The only thing that can change is the balance of probabilities.
Veteran readers will know that I took a lot of interest in the Chelyabinsk fireball that arrived on the same day that asteroid DA14 passed close to the Earth, and I wondered if they might have been companions. NASA said they weren’t: they were going in different directions, and it was just a fluke they arrived at the same time.
But eventually I found that a rock following about 10 million km behind DA14 could have passed very close to the Earth in 2009, and been thrown into a slow wide orbit that returned to the Earth on 15 Feb 2013, going in the same direction as the Chelyabinsk meteor.
But how probable was it that a rock could have been in the right place at the right time? I estimated that the chances of a single rock following behind DA14 being within less than 1 km of the exact right place in a tube of 100,000 km radius stretching from DA14 to the Earth were in the order of 1 in 1017.
It was thus extremely highly improbable that a rock would be in the exact right place to strike the Earth. In fact it was more or less impossible.
But that’s just using one rock. If there were lots and lots of rocks trailing in an evenly distributed cloud between DA14 and the Earth, the probability of any one of them landing on Chelyabinsk was much greater.
In fact if there were 1020 such rocks, the probability of one or more of them landing on Chelyabinsk approached 1. And it was then almost certain that at least one rock, maybe more, would land on Chelyabinsk.
How likely it was that a rock trailing behind DA14 could have landed on Chelyabinsk largely depended on the [unknown] density of a rock cloud trailing behind DA14. If you think there are very few such companion rocks, then it will seem highly improbable to you that one of them would land on Chelyabinsk. But if you think there are lots of rocks, then it will seem almost certain to you that one would land on Chelyabinsk.
So with a slight change in assumptions the impossible can become certain, or the certain become impossible.
I wonder if the same is happening with the vanishingly small cancer risks associated with inhaling any concentration of tobacco smoke (bearing in mind that tobacco smoke is a sort of cloud of tiny rocks). In one presentation of the facts, the danger of any particle causing cancer can be dismissed as negligible. But with a slight change in the underlying assumptions, tobacco smoke in any concentration may perhaps be shown to invariably cause cancer.
I’m beginning to think that the problem may lie in statistics itself, and that once statistical arguments are employed for or against any proposition, the result is deadlock.
The same sort of problem applies to the use of statistics in quantum mechanics, as illustrated by Schrödinger’s cat:
a cat, a flask of poison, and a radioactive source are placed in a sealed box. If an internal monitor detects radioactivity (i.e., a single atom decaying), the flask is shattered, releasing the poison that kills the cat. The Copenhagen interpretation of quantum mechanics implies that after a while, the cat is simultaneously alive and dead. Yet, when one looks in the box, one sees the cat either alive or dead, not both alive and dead. This poses the question of when exactly quantum superposition ends and reality collapses into one possibility or the other.
Anyway, a few months ago I managed to ask NASA whether they thought there could be rocks accompanying asteroids like DA14, and they told me that there was no chance of any whatsoever, because only comets had companion rocks lying along their orbits (which cause meteor showers), and asteroids had none. It appears that NASA’s definition of a asteroid includes having no companions. So they can’t possibly contemplate any companion rocks, and this was perhaps why they declared that the two events were completely unrelated within hours of first reports of them.