Gratuitous Mathematics

Thursday 1 December 2005 at 7:11 pm | In Articles | 4 Comments
    \displaymath q_x=1-e^{-\int^1_0\mu_{x+t}}\:dt
    The meaning of life? (Not quite but this formula will tell you much of it you have left*)

That’s how the Guardian today publicised its article on life expectancy. It then attempted to ‘explain’ the formula with a tiny note saying *Details overleaf. These ‘details’ were:

    The force of mortality at age x is defined as: \mu=GM(r,s), with parameters a_1,\dots,a_r and b_1,\dots,b_r fitted by maximum likelihood. For example, GM(2,3)=a_1+a_2 t+e^{b_1+b_2 t+ b_3 (t^2-1)} where t=\frac{(x-70)}{50}. The the equation above shows the probability that someone aged x will die within one year. Still puzzled? See page 8.

On page 8 is the article So, how long have we got? which sheds no light on the formula; it doesn’t even mention it.

So why was this formula there? To make the journalist or the paper look clever? Who knows. But it certainly is completely useless even to mathematicians. The example just makes the whole thing even more obscure. Wouldn’t it be nice to have more mathematically trained journalists who wouldn’t just show off but instead make things clearer?

4 Comments »

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  1. Hey, do you have some time to help a guy out? I’ve got a real hard Algebra 2 problem. The thing is I have to find a standard form quadratic equation that contains the points (6,-9), (-3,18 ) and (12,-57). If you could help me out, you’d be a real life saver, thanks. Seta.

    Comment by Seta A. — Sunday 4 December 2005 4:15 am #

  2. The standard form for a quadratic is y=ax^2+bx+c. You have 3 sets of values for x and y which you then put into the equation to get:

    \parbox{5cm}{\begin{eqnarray}
-9&=&36a+6b+c \
18&=&9a-3b+c \
-57&=&144a+12b+c
\end{eqnarray}}

    You must solve these simultaneous equations to find a, b and c. Do this by subtracting (1) – (2) and (1) – (3) to get simultaneous equations in a and b which you should be able to solve.
    Don’t forget to check your answers in the 3 equations so you spot any errors.

    Comment by Steve — Sunday 4 December 2005 11:19 am #

  3. Hi Steve, I too was bloody annoyed with that formula in the Guardian. I wrote it up on the blackboard ready to calculate when we were all due to die, and then tried to make sense of the instructions. They seemed to give an example of some numbers to stick into it, but didn’t explain how to generalise that for any numbers or variables or whatever you liked.

    All very confusing…

    Comment by Craig — Thursday 8 December 2005 9:49 pm #

  4. The only solution to this would be to persuade mathematics graduates to go into journalism. But would they be welcomed, even if they wanted to have such a career?

    I still remember, about 20 years ago, when a quality newspaper published a claimed proof of Fermat’s Last Theorem. Yet any moderately qualified mathematician could see that it had merely ‘reduced’ the countably infinite number of possible counter-examples to check to another set of countably infinite possibilities.

    Comment by Steve — Thursday 8 December 2005 10:12 pm #

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