The big argument: Are there more fruit or doors?

6 December 2023

Fruit, argues Sophie Maclean

Given the grape article about Fermi estimation in this issue, I’m sure that’s how you’ll be expecting me to win this debate. Lime going to have to disappoint you. I’m going to app(eal)le to semantics here, and discuss what we define as a ‘fruit’.

The word ‘fruit’ comes via old French from the Latin ‘fructus’ meaning ‘enjoyment of produce’. With this ancestry, I posit that, in fact, anything that is not naturally occurring is a fruit. Indeed if this weren’t the case, the commonly used phrase ‘fruits of one’s labour’ would be nonsense. All doors are manmade, ergo all doors are fruits.

But wait, what about The Doors? I am yet to show that those four doors are fruits! Fear not. The Doors all are the fruits of their parents’ loins, so they are indeed also fruits. Enjoy that mental image.

So all doors are in fact fruits. And it’s true that not all fruits are doors. For example, consider the humble pear. A fruit, for sure, but not a door.

This is a maths magazine though, so I’ll write this in mathematical terms to appease the inevitable protestors:

\[\left\{\text{man-made objects}\right\} \subseteq \left\{\text{fruits}\right\}, \; \left\{\text{members of The Doors}\right\} \subseteq \left\{\text{fruits}\right\}\]
\[\implies\]
\[\left\{\text{doors}\right\}\subseteq\left\{\text{man-made object}s\right\} \cup \left\{\text{members of The Doors}\right\}\subseteq \left\{\text{fruits}\right\}\]

\[
\text{pear} \in \left\{\text{fruits}\right\}, \; \text{pear} \not\in \left\{\text{doors}\right\} \implies \left\{\text{doors}\right\} \not\subset \left\{\text{fruit}\right\}.\]

Therefore
\[\left\{\text{doors}\right\}\subset \left\{\text{fruits}\right\} \implies \left|\left\{\text{doors}\right\}\right| < \left|\left\{\text{fruits}\right\}\right|\] $\square$

Doors, argues Michael Cavaliere

Think about all the doors you encounter every day! The easiest place to start is the most obvious type of door: residential doors. Houses have all sorts of doors: front doors, back doors, all the internal doors, cupboard doors, fridge doors, oven doors, microwave doors. I could go on.

8 internal doors $+$ 2 external doors $+$ 12 cupboard doors $+$ 4 kitchen appliance doors $=$ 26 doors per house. Then:

\[\frac{\text{8 billionn people}}{\text{4 people/house}} \times 26\; \text{doors}/\text{house} = 52\,\text{billion doors}.\]

That’s 52 billion doors, just in the residential buildings of the world. With 1.5 billion vehicles in the world averaging four doors each, there’s another 6 billion doors sat in the driveways of those houses.

Of course, those aren’t all of your everyday doors. Over half of the world’s population are working-age adults, each of whom goes to a workplace every day with plenty more doors.

(1 office door + 6 cupboard doors) $\times$ 4 billion workers = 28 billion doors.

And we’ve not even considered hotel doors, locker doors in gyms, or Advent calendar doors.

I’m starting to lose track now but I think I’ve made my point. At the end of the day, all I know is that my student house has several doors and not a single piece of fruit in it, and that’s convincing enough for me.

Sophie Maclean

Sophie Maclean is a recent maths graduate from the University of Cambridge and very much misses her degree. She has no free time—she is a Chalkdust editor.