Innumeracy and the cult of anti-vax

The last post was about an innate understanding of scale and scope, and how this lead to a general understanding of magnitudes.

A real world example, and one that is top of the news lately is the whole “anti-vaccine” movement. This is the increasing tendency to choose to not vaccinate your children due to the faulty belief that vaccines are worse than the disease. Leaving that argument aside, lets apply this “scale” thing to the antivaccine argument:

Measles, a once common childhood disease, has several bad results, with the death rate being on the order of 3 per 1,000 infections. (I will admit that I am horrified by how high this is.) That means that if 1000 children contract the measles virus, 3 will die. Let that sink in. That is a 0.3% fatality rate. Seems pretty low, until …

The MMR (Measles, Mumps, and Rubella) vaccine has pretty much eradicated the disease. In 2000 there were virtually no cases reported in the USA.

Of course, the vaccine is not risk free. The major risk is an allergic reaction to an ingredient, usually the albumin (protein from the white of an egg), causing an anaphylactic reaction. This is somewhat on the order of less than one event per million doses. That is almost three orders of magnitude lower than the risk of death. (1/1000 the risk). And guess what, when you get a vaccine, the healthcare provider has an epi pen ready for the vanishingly rare anaphylaxis, so even if you do have such a reaction, you will get immediate treatment for it. There is also a more common reaction, of a fever, a rash, and other symptoms, all of which are far less risky than the disease. None of these are considered life threatening.

So, the risk of a vaccine adverse reaction is 1/1000th the risk of DYING from the disease itself.

The truly horrifying statistic is the rate of death in immunocompromised victims of measles. That mortality rate is a staggering 30%. That means that if your child is immunocompromised, and contracts the disease, they have a nearly 1 in 3 chance of dying.


The general population is poorly prepared to weigh risks, and scale. Clearly, the benefits of vaccinating your children vastly outweighs the risks with vaccination, but the specious arguments bantered about highlight how little
the general populace understands the scope and scale of the risks.

Numeracy, the common sense of numbers

When I was in school, calculators were new enough, that they really weren't something that the average student had. They were expensive, and quite limited. Hence, we learnt how to do arithmetic with pencil and paper.

In those days, the lesson plans were written to be approachable in a reasonable time frame to students to solve problems with pencil and paper easily.

Even in my physics class (3rd year) we never once used a calculator. But I did learn some things that hang with me to this very day.

Scale – in high school mathematics, it isn't obvious, but when you take science courses, you learn about this thing called "Scientific Notation". That is typically, mantissa and an exponent. The mantissa being a number like a.bbbbb where the number of "significant digits" is related to how precisely you know a value.

Estimation – In my high school physics class, we didn't use calculators, but we did learn how to use a slide rule. Don't laugh, this was extremely useful. You learn that you can quickly do large calculations by just operating on the mantissa's and then figuring out the magnitude. Thus 6.03e23 * 1.47e-7 is the equivalent of (6.021.47)x1023 – 7 or 8.85e16 (note, if you use a calculator to calculate 6.02×1.47 you will get a lot more numbers to the right of the decimal point, but I truncated it at two, as there was two digits of significant figures). Thus you can quickly get the scale of the answer (or estimate) by fiddling with the exponents. In this case, you can also get close to the mantissa by noting that 6.02 is almost 6, and 1.47 is a little less than 1.5. 1.56 is 9, so you know that it is a little less than 9, so guess 8.8, and then the exponent of 23 – 7, and you get 8.8e16, pretty damn close, and you can do it in your head.

There are a lot of other tricks that I use almost daily, often to claims if being magic by the people I interact with, but reality is just common sense combined with numeracy.

Today, students are armed with calculators, and the art of estimation, and an innate sense of scale is dying. I firmly believe that, plus the rise of misinformation packaged as fact on the internet is leading to the rise in the anti-vaccine trends.

Next up, I will take apart the common justification of not vaccinating.