How Joanna Blythman got it wrong, part 2

If you haven’t seen it yet, you will need to read part 1 first to understand what is going on here.

Let’s start with Blythman’s early paragraph about the merit of scientific inquiry;

Like many scientists, he thinks he deals in absolute fact, offering a rock-solid “evidence-based” scientific “truth” that trumps all other perspectives – social, moral, political – and which is superior to other types of knowledge we might bring to bear on our decisions, such as intuition, experience, observation, or even common sense.

Actually, it is. Intuition, experience, observation and common sense are all very well, but all of them are inevitably coloured by the subjectivity of the individual. Scientific enquiry is all about eliminating subjective elements to uncover objective truths.

Common sense would tell you that the World is flat, because (barring the odd lumpy bit such as the Himalayas or the Cotswolds) it looks flat, especially at the coast. Inductive reasoning would lead you to think, “well, hang on… if I see a ship appear over the horizon the mast is visible before the hull. So maybe the sea isn’t flat but very slightly curved.” Common sense would certainly lead you to suppose the Sun travels round the Earth.

Many of the findings of mathematics or science are counter-intuitive. A classic example is the Monty Hall problem.

Suppose you’re on a game show and you’re given the choice of three doors. Behind one door is a car; behind the others, goats [that is, booby prizes]. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one randomly. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you “Do you want to switch to Door Number 2?” Is it to your advantage to change your choice?

As the player cannot be certain which of the two remaining unopened doors is the winning door, most people assume that each of these doors has an equal probability and conclude that switching does not matter. In fact, the player should switch—doing so doubles the probability of winning the car from 1/3 to 2/3.

Thanks to Wikipedia for that

To emphasise the counter-intuitive nature of this paradox it is worth pointing out that when Parade magazine published the problem and solution (admittedly in a truncated form which was slightly ambiguous), many graduates including mathematicians wrote in complaining that the solution was wrong.

You might think about this if you’re ever a contestant on Deal or No Deal. With all the variables of so many prizes involved intuition is bound to trip you up.

Quantum mechanics is more or less an affront to common sense, but without it there would be no transistors, and eventually no digital computers. Without digital computers there would of course be no World Wide Web. So we have the delicious irony that you can view the Sunday Herald’s website via a medium which no knowledge system other than science could produce, where you can read Joanna Blythman denying the special status of science ahead of other knowledge systems.