The disconnect between the ubiquity of probability in our culture, especially in relation to health and illness, and the poverty of understanding of this area of mathematics strikes me as highly problematic. If one goal of eduction is to prepare our children (and ourselves) to participate in the world, then a solid understanding of probability should definitely be included.
But, as my opening statement suggests, while the world offers many opportunities to delve into the topic in relevant ways, it offers few guides to understanding. There is a lot of misinterpretation of statistics out there that a good education should equip us to recognize and counter.
Take, for example, the relationship between a particular illness and various factors that seem to be correlated with the incidence of this illness. If we exercise regularly, eat well, scorn smoking, and drink moderately should we feel cheated if we develop heart disease? Does the fact that we might die of heart disease anyway mean that none of these behaviours are worthwhile? Or, in the famous example, if one might smoke all ones life and still live to 97, does that mean that the relationship between smoking and lung cancer is all smoke and mirrors?
No. Most of this health information, and there is lots of it out there, is based on epidemiological studies. Epidemiology is the study of population health. It uses statistics to calculate the correlation between various diseases and various possible contributing factors. It does not determine cause. It determines probabilities, which can also be called risks. Just as individuals do win the lottery, despite the long odds, some smokers will live to 100. And some people who “do everything right” will get cancer.
What most of this health reporting is telling us is that there are correlations, sometimes strong correlations, between certain behaviours or characteristics and certain illnesses. Correlation is not cause. Human bodies are incredibly complex. Despite the enormous advances in scientific knowledge in the past 100 years or so, we still have very little idea of how that complexity works. Because of that, we know little of cause.
We do know that viruses cause the flu. And we know how viruses are transmitted. We only know in the most general terms why some people exposed to a virus will get sick and others will not, and why some will get sicker than others. We know that those things are correlated with factors like age, general state of health, diet, etc. And we can calculate the relative risks. But we don’t know exactly why.
So much of the current health debates seem to misrepresent these basic facts. There is a tendency to try to allocate blame to individuals for their illnesses. There is also a tendency to think that we should be able to eradicate illness. If only we all ate properly, no one would have heart attacks. The fact is that the probability you will die sometime is 100%. The part that is difficult to predict is when and how.
For those who want to learn more about probability, I recommend Chapter 2 of Nathalie Angier’s The Canon or Chapter 7 of Keith Devlin’s The Language of Mathematics. The archived radio programme on the history of probability from the BBC’s In Our Time series, is also informative. Devlin’s chapter also has a lot of history in it. There is also good list of readers for various ages at Living Math.