Posted by
Andrews on Wednesday, August 19, 2009 2:25:15 PM
I have written often on how numbers can be misused, but I stumbled upon a particularly obvious example, and one that is rather amusing as well.
The
paper in question is a slightly tongue-in-cheek study
by Munz, Hudea, Imad and Smith? (the question mark is part of his name), examining the outcome of an outbreak of zombies. However, despite the silly topic, they claim the paper illustrates a serious topic, modeling of disease outbreaks. And so, I don't feel bad picking apart a truly absurd conclusion in the paper.
The point in question comes from the fourth page of their article where they say that S'+Z'+R'=Pi. That means the increase in living, zombies and dead at any given time equals the birth rate. And as a result, as time approaches infinity, S+Z+R equals infinity. Their conclusion is what is absurd:
Clearly S [does not equal infinity], so this results in a ‘doomsday’ scenario: an outbreak
of zombies will lead to the collapse of civilisation, as large numbers of people are either
zombified or dead.
That sounds superficially sound, and obviously took in the BBC writer who wrote about this article, but if you think about it, their conclusion does not follow.
To see why, think about this without zombies. The change in the number of living plus dead is equal to the birth rate as well, and the total of living and dead approaches infinity as time approaches infinity. And, once again, the number of living is not infinite, so the situation is exactly the same, but for zombies. Yet, we do not take the existence of the dead as showing society will collapse.
No, their conclusion is nonsense. If we assume a rate of infection from zombie to human of 0.01%, then there is no necessity that society will collapse, and their conclusion is shown for the nonsense it is. Their argument here is both incorrect and lazy.
But it got them into the BBC news pages, so I guess that makes it successful.
POSTSCRIPT
My earlier writing on misleading numbers, in more serious contexts can be found in "
Another Example", "
The Devil is in the Definitions (And Assumptions)", "
Bad Logic" and "
Yet Another Needless Scare" and the links in the postscripts to those articles.
POSTSCRIPT II
What makes their argument more amusing to me is that it reminds me strongly of the absurd simple formulae Keynes so often sued to justify the most insane of his theories. To see them used here in a remarkably similar invalid "proof" brought back many memories of trying to figure out why anyone took Keynes seriously.
POSTSCRIPT III
This reminds me of another absurd "proof" I read arguing time travel is impossible. Their argument was that "time per time" would produce a measurement without units. The problem with this argument is twofold. First, unit-free measurements can be valid, for instance Mach has no units, as it is determined by dividing the speed of an object by the speed of sound, resulting in a measurement without units. So unit-free measurements are clearly valid.
Second, and more importantly, time travel does have units, it is measured in terms of "collective time per personal time". I do not mean to say I believe time travel to be possible, but if it were, the way to measure the speed of time travel would be how many seconds of collectively perceived time pass per second of time as measured by the traveler. For instance, if in what I perceive to be a minute I go from 2009 to 1009, I am traveling at 1000 collective years per personal minute. The two differing types of time mean there is a unit.
But enough of silly articles making absurd points. My purpose here was to show how even silly articles can often include misleading calculations. And, more significantly, how often journalists are taken in by formal mathematics, even when the conclusions are utter rubbish.