I was recently in a meeting and we were discussing failures – failures of structures such as pipelines. The chances of a pipeline failure, and causing a fatality were put forward, and a figure of 1 chance in 1,000,000 per annum of being killed by a pipeline failure was considered acceptable or ‘tolerable’ by risk experts.

Then a comment was made about ‘zero failures’, and how we all wanted ‘zero failures’, and the general public will reject figures such as 1 in 1,000,000, preferring the much simpler ‘number’ called ‘zero’. The general public take a very subjective view on risk, whereas risk experts take an objective view. In simple terms, when a risk expert gives a chance of 1 in 1,000,000, he/she is focused on the ‘1’ and the ‘1,000,000’, whereas the general public is only focused on the ‘1’….

The discussion then moved onto ‘zero risk’. If the general public want ‘zero risk’, meaning they want no harm caused by a pipeline failure, or no pipeline failures, they are asking for ‘zero failures’.

The risk experts said we could never reach zero, but could aim for a very small number. We were now talking about a lot of ‘zeros’.

I understand what a ‘failure’ is (something breaks…), and I think I understand what ‘risk’ is (the chance of an event and its effect). But I’m not too sure what was meant by ‘zero’….

Why? This short blog post explains why….

## ‘Zero’ started as ‘nothing’

‘Zero’, meaning a number, is a relatively modern creation. Thousands of years ago, there was no such thing as ‘zero’. Our ancestors were very happy with their simple lives and did not need ‘zero’; for example, if they had three goats, they had… three goats. If they had no goats, they had… no goats. Why create a new term called ‘zero’. ‘Zero’ goats? ‘No’ or ‘nothing’ was quite sufficient.

We can move through the ages, and still no sign of ‘zero’. We all know Roman numbering: I, X, C, M, etc.. But there is no ‘zero’ in Roman numerals, and their numbering system was used throughout Europe up to the 15th century. The Romans were very clever, but did not need a zero: their numbering systems was developed as a means of trading and bartering. If there was nothing to buy or sell, there was… ‘nothing’. No number was needed.

The Romans were not alone in not needing a zero. The Chinese and Egyptians did not see a need for it in those ancient times. This all makes sense: the idea of zero actually existed, to describe ‘nothing’. ‘We have no goats’ does means ‘we have zero goat’. The latter doesn’t sound right, and if you have nothing to count… why count?

The concept of zero was certainly a good discussion point. The Greeks dismissed zero, as it was not mathematically correct. Aristotle (384 BC-322 BC)) was an impressive Greek mathematician (he studied under Plato (428 BC-348 BC)), but he did not like the idea of zero as a number: you can add (3+0=3), subtract (3-0=0), and multiply (3×0=0) by zero, but it did not make sense when you divided by zero (3/0=0). A number divided by a very small number, should give a huge number (infinity?). And Aristotle was very worried about 0/0=0….

In summary, our ancestors did not use ‘zero’, as they had… ‘nothing’. ‘Nothing’ is a concept, the same as the concept of ‘infinity’: both ‘nothing’ and ‘infinity’ are difficult to visualize….

## ‘Zero’ became a ‘placeholder’

History tells us that zero was first used in Babylonia (now Iraq) or India, but it was used as a ‘placeholder’; for example, how do we write five hundred and two? 5something2? A ‘zero’ symbol makes sense. ‘502’ means 5 hundreds, no tens, and 2. The zero indicates no units wherever it is placed – it is the absence of a number. A placeholder makes sure digits were in the right places, but it had no numerical value.

Originally, zero was indicated by a dot: ‘.’. It later inflated itself and grew into a ‘0’ – a mathematical symbol – thought to symbolize the ‘circle of life’ – but not a number.

In summary, zero was first used mathematically, as a ‘placeholder’, although it still meant ‘nothing’ (no number in that place). Zero was not a number.

## When did ‘zero’ become a number?

The Hindus are generally acknowledged as being the first to formulate zero as an independent number. It has a value between +1 and -1. A number in its own right. Zero had graduated from being a nothing to being a number

Zero was needed: it could no longer mean ‘nothing’. If zero means ‘nothing’, how can we have negative numbers? Something less than nothing? The absence of a zero was causing many other problems; for example, ancient calendars did not have a year 0. There was 1 BC followed by 1 AD. Also, the old Catholic church did not accept either zero (‘nothing’) or infinity, as they saw them as challenging the existence of God. The belief is that God is in everything that exists; therefore, anything that represents nothing must be satanic, and if you believed in zero you were a heretic and risked being burnt at the stake….

Zero was needed and accepted as we started to develop our understanding of mathematics (particularly algebra and calculus) five hundred years ago, and now it is essential in our world of mathematical formulae and computing – perhaps it is the most important ‘number’ we have?

## Zeros are important

We now know that ‘zero’ can be:

- A concept, meaning ‘nothing’;
- A placeholder in a numbering system;
- A number between +1 and -1.

Zeros can be very good, and certainly do not mean ‘nothing’; for example, I would rather have $1,000,000 than $1,000. The more nothings you have, the more money you have….

Today ‘zero’ is viewed as a number, but it is still also a concept, and a very strange concept. If I stand close to you, but don’t touch you, then there is nothing between us. But… if there is nothing between us, we must be touching? ‘Nothingness’ is difficult to visualize or believe – even a ‘nothing’ such as a perfect vacuum can contain light waves or magnetic fields. Does ‘nothing’ exist?

## Summary

Zero is a very interesting concept/placeholder/number. It is difficult to visualize, but is needed to make mathematics, and the world, work.

When we talk about ‘zero risk’ or ‘zero failures’ we are hoping to eliminate all risk or all failures. We know that risk can never be zero: if we could practically reduce a risk to zero, we could all live forever (zero risk of death from any cause). Everything has a chance of failing. So, if we want ‘zero’ pipeline failures, or ‘zero’ risk from pipeline failures, we must stop using pipelines.

We need engineering structures such as pipelines, so we cannot eliminate them, or their inherent risks, but stating a number to the general public of, say, 1 in 1,000,000 chance of being killed by a pipeline failure will cause concern, as nobody wants to be killed. Experts like numbers, and like the probabilities and risks generated by analysis, but the general public base risk assessment on emotions, and fears, and their view of life and risks. When the general public want ‘zero’ they want ‘zero’, but we cannot give them this ‘number’.

So, be aware… if you quote ‘zero failures’ or ‘zero risk’ you are promising to deliver the impossible, but it would have been far worse for you back in the 15th century – you would have been burnt at the stake for heresy….

## Internet sources

- https://www.theguardian.com/notesandqueries/query/0,5753,-1358,00.html
- https://www.smithsonianmag.com/history/origin-number-zero-180953392/
- http://www.bbc.co.uk/news/uk-england-oxfordshire-41265057
- https://www.bbc.co.uk/education/clips/zt96n39
- http://www.bbc.com/future/story/20161206-we-couldnt-live-without-zero-but-we-once-had-to
- https://yaleglobal.yale.edu/history-zero
- https://www.nytimes.com/2017/10/07/opinion/sunday/who-invented-zero.html

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