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Twenty years ago (or thereabouts) there was a Christmas road safety
campaign in which they said:
On the surface you might think that sounds reasonable, but I thought "Hang on a minute. If having a seatbelt doubles your chance of survival, that means your chance of surviving without a seatbelt has to be less than 1/2."
You see, it's not possible to have a probability greater than 1, so doubling your probability can't take you above 1, so you can't start above 1/2. So the statement, as made, is obvious nonsense.
To a mathematician.
A moment's thought shows that we could instead say:
Actually, I think that's more powerful, and it's no longer obvious nonsense in the same way as the original is. In fact, I can easily see how it started in this way, which I can imagine is what the statistics approximate, and then some advertising person with no mathematical ability, and proud of it, converted it to the obvious nonsense.
"So what?" you ask.
More recently I saw this:
Well, yes, funny, but again, with my mathematical hat on, it's not just nonsense, it's obvious nonsense. What would be the constant of proportionality? It would have to be greater than zero, reality tells us that, but then we have:
And now again, because probabilities can't be bigger than 1, we have a problem. The direction-giver is limited as to how many times they can say "You can't miss it", and we know from real life that that's just not true - they can say it as often as they like.
And again, we can turn this around and make it something that's not manifest nonsense, by saying:
Now we can see that every time the direction-giver uses the magic phrase, your chances of success go down. This is just as funny, just as pithy, and has the merit of being mathematically sound.
"So what?" I hear you say again.
"What does it matter?" I hear you say.
"It's just a joke!" I hear you say.
Bear with me for a moment - this will seem like a stretch, but I am going somewhere with it.
You see, I've become really sensitive to the issues of role models in mathematics, science, technology, engineering, and programming. Someone coming out of the cinema after seeing the recent Star Wars movie was heard to say:
"At last I've seen someone use a light-saber who looks like me."
Yes, the speaker was black.
Nichelle Nichols, who played Lt Uhura on Star Trek, wrote this:
We know that role models are important in deep and subtle ways. We know that we have to show a wide variety of people doing maths, science, technology, engineering, programming, and more, because people need to see people like them doing these things.
We need to remove the barriers.
Little by little, small pushes that are all in the same direction can lead to a huge, overwhelming net effect. Physics tells us that, and it's clear that something very similar is true in sociological contexts as well.
Wow, that got serious, didn't it? All because of something that was said in jest, intended to provoke a laugh?
Yes. And in response to that, I'm reminded that the bullies in the work place, when challenged, often respond with "It was a joke!" Or "Come on! Lighten up!" Or "You need to grow a thicker skin."
It can be relentless, subtle, sinister, and insidious. We are becoming more aware of how these small, small, subtle digs can have an eventually overwhelming effect.
And now I'm beginning to wonder about things like the two instances I started with. If people accept things like "double your chance of surviving" and "chances are directly proportional to" then they are being drip-fed a way of thinking that is then totally at odds with real maths.
So here we are:
I'll bet that provokes a reaction from everyone who has ever tried to teach probability, and I'll bet it's not a happy one.
Come on! It's just a joke!
It may be that getting the maths right is no joke.
I've decided no longer to include comments directly via the Disqus (or any other) system. Instead, I'd be more than delighted to get emails from people who wish to make comments or engage in discussion. Comments will then be integrated into the page as and when they are appropriate.
If the number of emails/comments gets too large to handle then I might return to a semi-automated system. That's looking increasingly unlikely.
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