Numbers are part of our everyday lives and are often viewed in difficult conditions – you may only have time to glance at a number, or maybe the light is bad or you have a headache.
But mistaking one number for another can be the difference between a winning lotto ticket, getting called for a job interview or receiving a speeding ticket on your next get away.
So, how and why do we confuse numbers?
Number confusion can stem from their visual similarities. Visual features, like shared curvature (6 vs 9), openness (2 vs 7), and straight lines (1 vs 7) can lead us to easily confuse one number for another.
Alternatively, number confusion can stem from the numeric proximity of individual numbers. Numbers that are closer together on the number line, like 1 and 2, may be easier to confuse than numbers further apart, like 1 and 9.
But which of these two factors, visual similarity and numeric proximity, are responsible for me paying extra on my morning coffee? Knowing what causes number confusion can help us devise ways to minimise it.
Interestingly, the answer may not be in the numbers themselves but, instead, it may depend on who you are and what experiences you’ve had.
Culture and Number
Numbers can be largely broken into two groups: symbolic numbers that are visually distinct and can be used or combined to represent unique quantities; and non-symbolic numbers that physically represent their values.
Cultures around the world are very familiar with non-symbolic numbers, like dice patterns, tallies and playing card patterns. With non-symbolic numbers, like dice, one ‘dot’ corresponds to 1, while six dots mean 6.
But at a glance, telling seven dots from eight can be very difficult – they are both numerically and perceptually very similar. For this reason, symbolic numbers are widely used in the modern world.
In cultures like Australia and Taiwan, symbolic Arabic numerals 0 – 9 are commonly used for finances, timekeeping, speed and safety signs, as well as mathematics.
However, unlike Australia, it’s also common for Taiwanese to use simplified Chinese numerals 〇 – 九 (0-9) when conveying everyday quantities – like writing down how many apples you want from the shops.
Finally, there are a host of numerals used throughout the world that are uncommon to both Australians and Taiwanese – for example, the Thai numerals, ๑ – ๙ (0-9).
CROSS CULTURAL EXPERIMENT
For scientists trying to understand how and why we confuse numbers, Australian and Taiwanese cultures provide a rich avenue of study: Taiwanese and Australians are both very familiar with Arabic numerals and dot patterns; Taiwanese but not Australians are very familiar with Chinese numerals, and neither Taiwanese or Australians are familiar with Thai numerals.
In a joint collaboration between the University of Melbourne, the University of Newcastle in Australia, and the National Cheng-Kung University in Taiwan, our recently published research explores why people mistake one number for another, and how this changes between cultures.
In an experiment reminiscent of the game show, ‘Wheel of Fortune’, participants viewed a number between 1 and 9, presented in Arabic, Chinese, Thai, or as Dot numerals and identified it on a number wheel (see above graphic).
The catch was that each number was hidden in a patch of background visual noise that made the number easier or harder to see depending on each participant’s initial accuracy in identifying them.
Using a set of mathematical predictions and contrasting these to the rates at which each number was mistaken for another, we were able to visually represent the differences and similarities participants look for when mistaking one-number for another.
This technique is known as multidimensional scaling.
We were then able to rotate, scale and slide these visual patterns over one another to create a ‘matching solution’, known as procrustes analysis, and quantify how similar these multidimensional patterns were between the two cultures.
For Arabic numbers, familiar to both Australians and Taiwanese, numbers were confused by perceptual similarities – similar curvature (8, 3, 9) and openness (2 v 7) – with nearly identical representations.
For Thai numbers, unfamiliar to both Australians and Taiwanese, numbers were also confused by their perceptual similarities – similar curvatures and orientations – with nearly identical representations between cultures.
For Dot numerals, familiar to both Australians and Taiwanese, numbers were confused by their perceptual similarities and their numerical proximity; 1, 2, and 3 were commonly mistaken, as was 4 and 5, 6 and 7, and 8 and 9.
Importantly, these patterns were identical between cultures.
Finally, and most dramatically, for Chinese numerals, familiar only to the Taiwanese participants, numbers were represented in an entirely different way between cultures. Both cultures confused items by their perceptual similarities, but the confusion was caused by very different features.
Australians confused Chinese numerals by the number of line-strokes and the openness of the numeral.
In contrast, Taiwanese confused Chinese numerals by their line-alignment and by a second, unidentifiable dimension which held no relationship to the numeric value.
These results suggest that, when presented with novel stimuli like Thai numerals or familiar stimuli like Arabic and Dot numerals, different cultures view them in a similar way.
However, acquired expertise and familiarity with a set of stimuli, like Taiwanese being familiar with Chinese numerals, can quite literally change how we see the world.
This research highlights how important it is for us to remember that our experiences and cultures change how we view our surroundings, from how we understand safety signs and signals, to how we read information online – and yes, whether we spot our winning lotto numbers.
Knowing this, we can better teach people and design our world in a way that avoids mistakes between people and across cultures.
Dr Garrett’s co-researchers are Dr. Murray Bennett, University of Newcastle, Yu-Tzu Hsieh, National Cheng Kung University, Dr Zachary Howard, University of Western Australia, Dr Cheng-Ta Yang, National Cheng Kung University and Taipei Medical University, Dr Daniel R. Little, University of Melbourne, and Dr Ami Eidels, University of Newcastle.