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Numerical perception beyond observation

By Dónal - August 2018

Perception

Psychology

Can you really imagine one million of something?

“What are the chances of that? One in a million!”

It rolls off the tongue so easily but how many of us understand what ‘one in a million’ really is? We read statistics and rhyme off numbers and units every day – city populations, monetary values, distances to far off places, election votes, social media followers, technological capabilities, etc. We use large rounded numbers and generate an imaginative understanding of these numbers based on their relative divisors or multiples. And what’s wrong with that? Nothing at all, it’s a perfectly intuitive and logical approach and it gets us by just fine.

However there is a notable difference of understanding between the imaginative and the visual when it comes to numerical perception. Say you are asked to close your eyes and imagine three apples on a table; it couldn’t be much simpler, we’ve all observed three of a kind instantaneously. If you are now asked to imagine ten apples on the table, this too is easy to picture, based on our experience of encountering things in multiples of ten in everyday life.

Now suppose you’re asked to close your eyes again and imagine 3,174 apples all together in one shot. Suddenly you’re picturing a very large spread of apples in front of you, although you can’t account for every single apple within the required target. Even if you start with a small array and continuously add to or multiply it, at some point it becomes too busy and increasingly difficult to maintain a clean visual. It can only be deduced from this that at some point the imaginative numerical perception collapses and falls back on an intuitive estimation. A sort of cut-off point, probably different for every person and possibly based on many other circumstances.

Beyond this cut-off-point, to what extent is numerical perception skewed? Could it have real-world implications? To feed the curiosity, I posed a scenario of having one raffle ticket in a drum of one million tickets. Knowing my exact chances of winning, I tried to convert that ‘understanding’ into a measure of hopefulness or expectation based on pure intuition. It wasn’t a lot of hope to be honest, but it was important to get a measure of this feeling.

I came across this practical experiment carried out by Dr. Roger Steinberg at Carleton University in Minnesota to help his students gain a realistic understanding of geological time periods. Attaching 200 pieces of paper together each with 5,000 dots, he compiled a spread of one million dots that could be viewed instantaneously on one very large sheet of paper. In my scenario, each dot represents a raffle ticket in the drum – only one of which will be the winner.

Within seconds of observing the sheer vastness of dots laid uniformly across the paper, my ‘understanding’ of my chances of winning had been altered substantially. In this particular case, I became much less hopeful of winning having visually perceived the chances. What if cost was now introduced to the equation – would I enter the draw with my newfound understanding of ‘one in a million’? Surely, it would depend on the cost of the ticket and the prize in question, but in most cases… no, I wouldn’t enter. It just seems far too unlikely.

We don’t generally pay particular attention to this difference in numerical perception. Chances of winning a lottery is just one example where it could be a determining factor, but what about more serious matters in the field of politics, economics, or social sciences for example? Suppose a government is making long-term measures for a nation’s means of dealing with carbon emissions. The decisions to be made are based on big data gathered from years of research in climate change, as well as historical and forecasted economic data both on local and global scales. The people involved vary in their field of expertise, level of experience, and perceptual strengths. The resulting decisions would affect the individual, families, local businesses, all the way up to global corporations. Could the livelihood of a nation be effectively altered for the better or worse based on a misinterpreted perception of numbers?

I'm not a writer...

I'm not a writer, I'm a web developer. While I use this space as a platform to explore and share ideas and observations, some topics may fall short of my expertise, and as a result are open to correction. So if I've blatantly overlooked something, or even if you'd like to chip in your two cents on the subject, please do let me know!

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