Does Logic Work? Anti-Vax arguments to teach thinking…

I have this dream.  An educational resource to teach children to think: numeracy, logic, and how different an issue seems from an individual versus a population perspective.  In part, this is my response to anti-vaccine arguments that flourished following a 1998 Lancet article; but are as old as the first vaccine:

In 1796, Edward Jenner demonstrated that prior ‘vaccination’ with cowpox would lead to protection against smallpox.  Smallpox was one of the worst scourges of humanity, until eradicated in 1977 through a global immunization programme, led by the World Health Organization.

Anti-vaccine arguments date back to Jenner:  like most vaccines smallpox can cause serious adverse reactions, but it does not turn anybody into a cow – as depicted in the first image of the anti-vaccine movement.

I don’t know if anybody seriously believed that smallpox vaccine – cowpox that has been altered through multiple generations of human transmission – could turn one into a cow.  But the list of ills caused by modern vaccines, according to some anti-vaxxers, covers a large range of human illnesses for which we either have not yet defined the cause or there are multiple causes.

In fact, smallpox vaccine has amongst the worst safety profiles of vaccines.  Luckily for humans, this is now only of historical interest.  Smallpox was the first disease eradicated by a vaccine; though some anti-vaxxers can provide entertaining accounts of why it really has not been eradicated, or that its eradication was purely coincidental to the vaccine programme.

In 1999, I was invited to write WHO guidance on adverse events following immunisation.  The AEFI is a carefully crafted concept that requires understanding of the logical fallacy of post hoc, ergo propter hoc.  This is Latin for mis-attributing to coincidence a causal relation: when event A happens after event B, we can say that B caused A.

In reading through the science of AEFI, we classified events that happened after as being possibly, but not necessarily caused, by the vaccine.  The event could be from an error in storing, preparing or giving the vaccine: a programme error.  These remain too common in developing countries, the main audience for the WHO manual.  Injection and anxiety related reactions are relatively common, especially in poorly planned mass campaigns. But coincidental events are the main problem for immunisation programmes are those that just happen to occur after immunisation.  So, why is my claim for an event being coincidental stronger than the claim around smallpox eradication?

Of course, some AEFIs are caused by the vaccine. The known vaccine reactions have been well defined during initial trials; rarer events require wide-scale use in programmes to become evident. During my time leading the NZ immunisation programme, I found it ironic that the vaccine with the most severe known reaction (roughly 1 in a million risk of paralysis) was the one that caused the least public concern about vaccine risks. Perhaps because it was the only oral vaccine in the national immunisation schedule at that time.

In contrast, there is roughly a 1 in 200 risk of paralysis from infection with the poliovirus.  The risk difference between disease and vaccine is why immunisation improves health.  But human cognition is not well designed to compare risks.  For example, we worry more about getting on an airplane than in a car; while on a tropical beach we fear sharks more than a coconut falling on our head. (I hope that you know the first risks are statistically much lower than latter.)

So, you can see that our intuitive risk meter is off; but we can correct this through deliberate process of logical thinking together with careful review of the available evidence.  What I want is an education resource that helps children understand how to think in that deliberate process.  Which involves understanding numbers and logic, as well as the inevitable flaws in all kinds of data.  And the challenge of how to carefully appraise the evidence.  So, what does this education resource look like?

I look forward to contribution, as I explore these ideas, starting with the number one and how 1+1 can equal 0,1,2 or 3 – and the intrinsic ‘slipperiness’ of numbers.




Vaccines and numbers

The story of vaccines starts with a new child (is it you?) arriving into our strange quantum world; where particles come into and out of existence, by charm, spin or whim.

Each of the seven billion, or so, human beings alive at this space-time have this shared story.  It starts, when one (1) sperm joins one (1) egg & become (1) you. Did I just prove that 1+1 = 1?

But, 1+1=2.   Can both be true?  Yes, 1+1=2, has to result if the 1 refers to the same thing.  If not, it can also be 1+1= 3:  (1) Mum + (1) Dad  become a family of three, when you are born. And more as the family grows.

It all depends on both numbers counting the same thing.  In the case of sperm and egg, this is a special relation where both become a new thing: you!  There is also matter and anti-matter that together become nothing (1+1=0). (Strangely, this means that from nothing we can get something in the reverse process that is constantly happening in the sub-atomic world of this strange  quantum physics…


Why all this? To torture numbers?  The number is only valid, if the logic is correct.   If the logic is incorrect, the number is either meaningless, or can even mean the opposite.  It helps to understand numbers, if you want to understand vaccines.  Numbers can be used to confuse as well as illuminate.

In Propositional Logic, a statement of fact, or proposition, has Truth Value of  ‘1’ if ‘True’, and ‘0’ if ‘False’ . In Fuzzy Logic, numbers can also between 0 and 1, as this can better describe the world than the sharp categories that our minds make up.

So, what does number ‘1’ mean?  It defines the unit, the thing.  It is also the space between numbers – a unique role.  I hope you know all your numbers, but if you keep adding 1 you will never get to infinity, just a bigger number.  If you like big numbers let be introduce you to the Googol (10^100 or 1 with 100 zeroes after it) and Googolplex (10^Googol). The Googol alone is so unimaginably large that it exceeds the dimension of the known universe, nearly whatever units one uses.

So, you are 1 in 7 billion and more living breathing human beings on planet Earth-today.  One billion is a huge number:  (10^9 1,000,000,000).  It is biologically unprecedented for a single species to cover the entire planet. All of us from a small family that arose in Africa about 200,000 years ago, and survived climate change to emerge smarter.  Prof. Harari suggests that the Cognitive Revolution, about 70,000 years ago, led us to outcompete the other human species: at least half a dozen (which is 12; i.e., 6) that existed around that time.  From Africa, our ancestors left  about 50,000 years to progressively cover the planet, making countless species extinct as we rose to the top of the food chain through the organising capacity of language.

These are some numbers that can give you a perspective of your life, which is so short compared to these numbers, even smaller compared to the estimated age of Earth at 4.5 billion years.  The Bible gives us  ‘three score and ten’ or 70 years  (so how much is a ‘score’ – an old English measure?)  But increasing numbers of people are living over 80 or even 100 years; many in good health.  How long have you been here for?  And how long would you like to stay?  I often wonder if we go back to the place we came from, or this life is some small part of something that we cannot even comprehend.

Now, back to the start of your story.  A child is conceived (from the sperm and egg), grows in its mother’s womb for about 38 weeks and is then born on this planet.  The womb nourishes and protects you as that first cell divides and divides to become the trillions (10^12 or 1 with 12 zeroes).  Once born into the world, you are now exposed to the  risk of  bugs: microbial infections: bacteria, viruses and other parasites. You are born with natural defences against these, and also an immune system  that can be ‘trained’ to protect against specific bugs.

This is what vaccines do.  But first we must understand a bit more about bugs, and the germ theory of disease.