Why is it that everyone wants to be a millionaire but not many people ever say they want to be a billionaire? This got me thinking. Don’t people want to be billionaires? Of course, we do. It’s just that we humans are really bad at comprehending extremely large numbers. We are conditioned from a young age that 10 is larger than 0 and 100 is larger than 10 because we can quite easily visualise these numbers. However, when we start talking about 100 millions or billions, our inherent feel for numbers goes out the window.
Just as a thought experiment, how long do you think it would take you to count to 100?
If you count mississippily (which could average to about one number every second) it would take you about 1 minute, 40 seconds.
Ok, great. So how long do you think it would take you to count to 1 billion?
Now this is where things get interesting. Firstly, our assumption that we count one number per second falls away as we get to large numbers. Saying the number one hundred million, one hundred thousand, seven hundred and forty-two is a mouthful and is definitely going to take longer than 1 second to articulate. For argument’s sake, however, if we stick with the assumption that you can count one number per second (to make the calculation nice and easy) it would take you approximately 31 years, 251 days, 7 hours, 46 minutes and finally 40 seconds to count to 1 billion. That is a crazy, mind-boggling amount of time!
Even though we humans are not used to comprehending truly large numbers, in mine closure costing, working with hundreds of millions is not uncommon. In fact, it’s become the norm. Unfortunately, when we work with such large numbers, our legal/ moral responsibility to the environment (which we aim to rehabilitate) may be negatively affected. We therefore need to formulate ways to help us come to grips with large numbers.
Now, what if I asked you how accurately you thought I calculated the time it would take to count to 1 billion?
It’s so easy to accept a single whole number as the truth. However, I made numerous assumptions which could influence the certainty and variability of the calculation. For example, I assumed you would count one number per second. This cannot be true as it takes longer to say each number as it increases in size. I also assumed that we all count at the same speed, that English is your first language and that you know how to count to 1 billion. Yes, these assumptions are wild! However, we seem to do the same thing with our mine closure costing. We make single closure costing quantum calculations without a full understanding of the accuracy of our costs.
Is it not plausible that your mine closure costing calculations were off by 1%? One percent of a billion is 10 million! We should actually be conducting our closure costing calculations in a more probabilistic manner; we should take into account all of our variability and uncertainty and express our final cost as a distribution, with a certain accuracy and confidence interval.
In order to help us comprehend our large mine closure costs and empower us to use probabilistic thinking, data management and visulisation. Minage will discuss the following ideas in the form of a series of mini blogs looking into the following:
- Data and data visualisation (coming to grips with large numbers);
- Probabilistic thinking (how to run Monte Carlo simulations through your closure costs)
- Contingencies in closure costing (how to determine contingencies mathematically)
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