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Mental Models

Drawing a Line

The mental model of drawing an arbitrary line in a grey area to make a rule, often with a buffer zone to account for uncertainty and risk of dire consequences.

THE IDEA

DRAWING A LINE

Grey areas are often dealt with like bedtime – an arbitrary line is drawn somewhere in the grey area and a rule is made. Where you put the line in the grey area depends on how dire the consequences of the extremes are. If one of the extremes is very dire then the line in the grey area will probably need to be further away from that extreme, to give a buffer zone around it. For example, some roller coasters have a minimum height requirement for safety reasons. If you’re too small then the safety harness won’t fit around you enough to keep you safe. In that case the consequences are very dire (injury or even death) and so the limit should probably be at the tall end of the grey area, to be safe.

With the cake, I am trying not to get fat, so I should probably draw the line safely within the “most probably won’t make me fat” part of the grey area, rather than somewhere in the “might not make me fat but it’s not clear” part. This is especially true because I am liable to stray over my line a bit, so I should put a little buffer zone in to be on the safe side.

One contentious area of drawing lines I’ve had to deal with a lot professionally is grade boundaries in exams. In the UK system, students graduate from university with a degree that is classed as first class, “upper second” class, “lower second” class, or third class, otherwise known as first, 2:1, 2:2 or third. But where should the boundaries be drawn? I have spent long and contentious hours in examiners’ meetings battling this out, in what is essentially a futile exercise placing a line in a grey area. No matter where you place it, someone will argue that it’s unfair to the person just below it, and as a result the line tends to shift further and further down. There is no logical place to put that line. I think the only logical thing to do is get rid of the lines and publish either averages on a fully sliding scale or percentiles instead.

A more contentious grey area arises when talking about race. I will not call this “literal” black and white, because we’re actually all shades of brown and pink. As discussed in Chapter 4, Barack Obama is often called “black” although one of his parents was black and one was white. So arguably it’s just as valid to call him white. However, once we understand that “black” here is being used to mean “non-white”, we see why it makes some sense to call Obama the first black president of the United States. Which is to say, we have found the sense in which it makes sense.

Where should we draw a line between black and white? If we draw it nearer the white side, this could acknowledge that only people who look really white enjoy the privileges of white people. But it could constitute exclusion of anyone non-white as “other”. At least talking about white people and non-white people is a genuine dichotomy, where black and white is a false one.

When to use it

  • Setting a minimum age for social media accounts to protect children from online dangers, weighing freedom against safety.

  • Defining a threshold for 'high risk' in medical screening to balance false positives and false negatives.

  • Creating cutoffs for scholarship eligibility based on test scores, acknowledging the arbitrary nature of such boundaries.

  • Establishing speed limits on roads to balance travel efficiency and safety, with a buffer zone for enforcement tolerance.

FROM THEORY TO EVERYDAY LIFE

In practice

01

Roller Coaster Height Requirement

For safety, a minimum height is set for roller coasters. The consequences of not fitting the harness are dire (injury or death), so the line is drawn at the tall end of the grey area of safe heights, providing a buffer zone.

02

Cake Eating and Weight Gain

To avoid getting fat, one might draw a line on cake consumption safely within the 'most probably won't make me fat' region rather than the 'might not make me fat but it's not clear' region, including a buffer for straying.

03

Exam Grade Boundaries

In UK university grading, boundaries between first, 2:1, 2:2, and third are arbitrary lines in a grey area. No matter where placed, someone argues unfairness, leading to lines shifting downward. The author suggests abolishing lines in favor of averages or percentiles.

04

Racial Classification (Barack Obama)

Barack Obama is called 'black' despite being half white, because 'black' is used to mean 'non-white'. The line between black and white is arbitrary; drawing it nearer the white side acknowledges privilege but excludes non-whites as 'other'.

✳

A MOMENT TO REFLECT

Put it to work.

  1. Think of a grey area in your life where you have drawn an arbitrary line. Is that line placed with a buffer zone for safety? How might you adjust it?

  2. Consider a situation where binary categories are used (e.g., pass/fail). What information is lost by drawing a line? What alternatives exist?

  3. How might the placement of a line in a grey area be influenced by the severity of consequences on either side? Give a personal example.

CONTINUE THE CONVERSATION

Source texts

  • The Art of Logic How to Make Sense in a World that Doesn’t (Eugenia Cheng)
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