The certainty of the improbable

When you toss a coin, there is complete certainty that an event that is only 50% probable will occur. When you roll a dice there is absolute certainty that a 16.67% probable event will come to pass. It sounds trivial. After all the probability is only to distinguish between outcomes once it is certain that the coin will be tossed or that the dice will be rolled. Probability of an outcome is meaningless if the coin were not tossed or the dice not rolled. But note also that the different outcomes must be pre-defined. If you toss a silver coin in the air the return of a golden coin is not included among the pre-defined, possible outcomes. That a roll of the dice can result in a 9 is not “on the cards”.

Probability or improbability of an event or a causal relationship is meaningless unless the certainty of some more general event or relationship is certain. Moreover as soon as we define the event or relationship to which we allocate a probability, we also define that that event or relationship is permitted. It is certain that tomorrow will be another day. Only because it is certain can we consider the probability – or improbability – of what weather tomorrow might bring.  Suppose we define the weather as being either “good”, “bad” or “indifferent”. We can guess or calculate the probability of tomorrow’s weather exhibiting one of these 3 permitted outcomes. My point is that as soon as we define the improbable we also make it certain that the selected outcomes are all permitted. Then even the most improbable – but permitted – weather outcome will, on some day, occur. Not just permitted – but certain. If the improbable never happens then it is impossible – not improbable.

We use statistics and probabilities of occurrence because we don’t know the mechanisms which govern the outcome. If mechanisms were known in their entirety, we would just calculate the result – not the probability of a particular result. The very mention of a probability is always an admission of ignorance. It means that we cannot tell what makes something probable or improbable and even what we consider improbable will surely occur. An outcome of even very low probability will then – given sufficient total occurrence – certainly occur. The 2011 earthquake and tsunami off the Tōhoku coast was a one-in-a-1,000 year occurrence. The probability of it happening next year remains at one-in-a-thousand. But given another 1,000 years it will (almost) certainly happen again.

One of my concerns is that the use of statistics and probability – say in medical trials – is usually taken to imply knowledge, but it is actually an admission of ignorance. No doubt the use of statistics and probability help to constrain the boundaries of the ignorance, but the bottom line is that even the low probability risks will materialise. The very use of probabilities is always because of a lack of knowledge, because of ignorance.

In the beginning of December I was having a regular medical check-up and I was offered a flu-shot for the winter which I took. But I got to wondering why I did. The influenza vaccine is effective in about 50% of cases (i.e. 50% achieve protection). Around 5% – irrespective of whether they achieve protection or not – suffer some adverse reaction to the shot. Around 0.5% of the 5% (1:4,000 of total vaccinated) suffer a fatal reaction. In our little clinic perhaps 3,000 were vaccinated this winter. About 1,500 would have achieved protection and about 150 must have had some adverse reaction. Most likely one person has or will suffer a fatal reaction. I was just gambling that I would not be that one person. When some new drug is said to have a 1% chance of adverse effects it only means that it will certainly have adverse effects for 1 in a hundred cases. When that one person chooses to take that drug, he may be making the best medical choice possible – but it is the wrong choice.

A low risk for the multitude but a certainty for some. The chances of something improbable never happening are virtually zero.

Improbable – but certain.

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