Risk: mathematical and otherwise

Draft of essay commissioned for a special issue (June 2015) of the Mathematics Enthusiast entitled “Risk: mathematical or otherwise”. Still time to make changes so critical advice welcomed, especially from mathematicians.


What role might mathematicians have to play in the management of risk? The idea of turning a risk, a possibility of loss or injury, into a “calculated” risk, a quantified probability of loss or injury, is one that has obvious appeal not just to statisticians and mathematicians – but to large numbers of others who would like to know the probability of failure before pursuing some intended course of action.

Conclusion: even when risks can be calculated with great precision, they can only be used to inform judgment, but not substitute for it. And it matters who is making the judgment. Read more …


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  1. Rob Schneider says:


    What a terrific paper. Terrific. Beginnings of a new book I would say … Last paragraph a gem.

    1. for publication, watch the fonts
    2. You use “GB” as a country where in fact I believe it’s just a geographic feature (land on which Scotland, Wales, and England reside). Do you mean the country UK and is the data UK? or is related to just these three political entities?

    Thanks for the encouragement.
    Also thanks for your “quibbles”. Yes, I must sort out the fonts.
    I am a Canadian but even I know that GB is not a country. The problem is that the Department of Transport doesn’t. The data represented by the graphs come in its publication Reported Road Casualties Great Britain. They offer no equivalent series for the UK.
    Best wishes

  2. Adrian says:

    As a safety professional with a BSc in Mathematics I enjoyed this as much as any of your other publications. There is good feed for thought for mathematicians and engineers who as history has shown often miss some very fundamental concepts. I really like some of the quotes including ‘The numbers almost don’t matter.’

    I noticed the change in font which didn’t really bother me.
    At first I thought the reference to the 1970 Act was a slight error but when I looked more closely I could see this was the USA Act. I presumed the occupational safety stats would also be taken from the UK given the road stats were.

    Really nice read.

  3. Paddy LONG says:

    Looking forward to listening to your lecture at Jericho’s Brasserie on 21st April.
    My relevant background is in Tutoring Advanced Driving for RoSPA here in Cornwall.
    Yours Aye,

  4. Matthew Squair says:

    Hi John,

    Actually yes, there is something you might include in an appreciation of mathematical treatments of risk, the ergodic fallacy.

    Essentially when we estimate the likelihood of future events we rely on Pascal’s [arallel worlds theorem, where each possible outcome becomes an alternate future, from there it’s a simple matter to calculate likelihood using set theory and voila we have our probability.

    There’s nothing much wrong with this except that it just doesn’t work for any risk that we’d actually like to avoid. The flaw is that Pascal’s method relies on the assumption of ergodicity, e.g. that ensemble statistics (what we just talked about) is the same as time series statistics (e,g. where we take risks one day after the next).

    Of course in real life we only get one life, and if we bet our life and loose there’s no way we can benefit from all those parallel worlds where we didn’t. So for risks where we can loose and it will break the bank classical or Pascalian risk severely underestimates our exposure.

    I’m interested about this from a safety perspective:


    Ole Peters is the chap who identified this fundamental flaw. He’s more interested in it from a financial markets perspective.


    Either way this subtle flaw in the logic makes us a society of risk takers on the grand scale.

    Thanks for this. Too late to make changes as the essay is now “In press”, but an interesting issue (new to me) that I will look in to. JA

  5. Dr Albert Owusu says:

    Hi John & Matthew.

    Ii will interest you I believe to share my outlook in my paper to be presented at CICT-8, 2015 conference in Greece. It is entitled “Quantitative Risk Assessment- A Pragmatic approach.”

    Just to know the role mathematics can play in our understanding risk assessment towards its management.

    Comments to me directly.


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