Comment »Posted on Monday 28 July 2008 at 7:30 pm by Jacob Aron
In Getting It Wrong, Mathematics

One of my science communication pet hates is stories about scientists discovering “the formula for x”, where x is a successful sitcom, why people vote, or happiness, just to name a few.

The latest culprit is PR agent Mark Borkowski who claims to have found a “scientific formula” for fame. The formula itself is given as follows:

F(T) = B+P(1/10T+1/2T2)

where:

F is the level of fame;

T is time, measured in three-monthly intervals. So T=1 is after three months, T=2 is after six months, etc. Fame is at its peak when T=0. (Putting T=0 into the equation gives an infinite fame peak, not mathematically accurate, perhaps, but the concept of the level of fame being off the radar is apposite.);

B is a base level of fame that we identified and quantified by analysing the average level of fame in the year before peak. For George Clooney, B would be a large number, but for a fabulous nobody, like a new Big Brother contestant, B is zero;

P is the increment of fame above the base level, that establishes the individual firmly at the front of public consciousness.

Not that it really matters, but this is terribly unclear. A more correct way to write it would be F(T) = B+(1/(10T)+1/(2T^2))*P, eliminating any ambiguity as to what each symbol means, but as with all of these stories scientific accuracy is not high on the agenda. Borkowski has made the same two mistakes that always crop up in these formulas – unmeasurable variables and confirmation bias.

The unmeasurable variables in this case are F, B, and P. T is time, where the units of T are periods of 3 months – not exactly orthodox, but still completely measurable. F, B and P however are measures of fame, for which I know of no scientific units. Perhaps fame is measured in the units of star power – solar luminosity.

Yes, I’m being facetious, but it is an important point. One of the greatest tools available to a scientist are the standard units of measurement known as SI units. I’ll talk about them in more depth another day, but they include metres, kilograms, and seconds – quantities we are all familiar with. This common set of units allow scientists to communicate their findings in a meaningful way, and the results of not confirming your units can be disastrous, as NASA discovered when they mixed up feet and metres, causing an unmanned spaceship to crash.

The other problem, confirmation bias, is an interesting one. It basically amounts to “people believe what they want to believe”, and it’s definitely in action here. Borkowski wanted to match Andy Warhol’s 15 minutes of fame with his own 15 months of fame:

I started to wonder if Andy Warhol – an artist by calling but a master of the stunt and the soundbite – was right; does everyone get 15 minutes of fame? It occurred to me that it should be possible to look at fame statistically, to analyse the evidence we have all witnessed in the media, to see if fame’s decline can be quantified. The answer, I discovered, is that it can be, and that Warhol was partially right – but the first spike of fame will last 15 months, not 15 minutes.

In looking at fame “statistically”, it turns out that 15 months is exactly right! Well done, Borkowski.

This formula fits the data remarkably well, giving a precise numerical value to the 15-month theory: if I put in T=5 (corresponding to 15 months after the peak), it gives F=B+P(1/50+1/50), which works out at F=B+.04P. In other words, up to 96% of the fame-boost achieved at the peak of public attention has been frittered away, and the client or product is almost back to base level.

Of course, if you put in T = 6 (i.e. 18 months) you get F = B + 0.03P (rounding off the decimal point). Three months later, it appears our Big Brother contestant hasn’t really got much less famous than they were after 15 months. What about after two years, when T = 8? In that case, F = B + 0.02P – fame doesn’t really appear to be dropping off very quickly, does it? The claim that ‘the study showed pretty conclusively that any specific boost to fame is sustained for approximately 15 months…’ isn’t remotely conclusive – in fact, I’ve just show that you can reach an entirely different conclusion by choosing different values of T.

The reason I hate these formula stories with a passion is that they damage the public perception of science. The ideas they offer are meaningless, suggesting that all scientist do is sit around dunking biscuits in a quest for perfection. That story is nearly a decade old, so the junk equation is clearly not a new concept, and I don’t think we will be rid of it any time soon. So, the next time you see an article proclaiming that science has once more advanced, and we now know how to calculate the cuteness of puppies or the magic of rainbows, please do the only sensible thing – ignore it.


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