one of the top 5 things I wish average people had a better grasp of is that the size of a number is contextual. a number’s bigness or smallness is not a fixed property of the number itself, it depends on what that number represents.
when you were a kid, a thousand seemed like a very big number. did you ever count that high? pretty tedious, isn’t it? it’s a massive number of toys to own, or dishes to wash, or people to meet. for most of the countable things you interact with in a normal day, a thousand is a big number. but in other contexts, a thousand can be a small number. It’s a tiny number for the population of a town. it’s a smallish number of dollars – if you only make a thousand dollars a month (in a wealthy country), you’re poor. it’s an utterly minuscule number of bacteria in your body, or dollars in a government budget, or grains of sand on a beach. a thousand of something might be a lot, or might be a little – it depends on what you’re counting, in what context.
most of the time, 0.1% is a pretty small number. if 1 in 1000 eggs has a double yolk, you probably won’t eat very many double-yolk eggs in your lifetime, unless you seek them out deliberately or eat vastly more eggs than the average person. if 1 in 1000 homes in your town have garbage disposals, garbage disposals are very rare where you live. but if a cosmetic surgery had a 0.1% risk of lethal complications, most people would see that surgery as unacceptably dangerous – 0.1% risk of death is a big number.
we’re not very good at thinking at scale. we’re especially bad at thinking about our fellow humans at scale. suppose that 0.1% of the population has some trait X. if you assume that none of the people you meet have trait X, you’ll be right 99.9% of the time. when you crack a joke about trait X at a party, there probably won’t be any X-people around to be offended by it. but 0.1% is 1 in 1000 – how big is that number, really?
it’s about 335,000 people in the US, for starters – the population of a small city. throughout your education, you probably had multiple classmates with trait X. there’s a handful of them at any large school. a medium-sized company will probably have several trait X employees. you might not know someone with trait X personally, but it’s a virtual certainty that someone else you know does. if you have a modest online following, several of your fans have trait X. if trait X were a disease, it would be too common to count as “rare”.
the next time you see a number you think of as “big”, like a million, I want you to stop and consider what’s being counted: does this number represent a large quantity here? compared to what? when you encounter a small proportion, think: how frequent is that, really? what’s the denominator (0.1% of what)? can you think of something comparable that happens about as often? is this number surprising?
Tags:
#yes this #death tw? #fun with statistics #(”fun” isn’t quite the right word‚ but that’s the category tag)
Brinens and Things 