One other way to map both types of linguistic statement consistently to math is to interpret "9x" as "there is a 9 times difference between these two things" and then "smaller"/"larger" tells you which end of that separation the subject is (rather than specifying whether the multiplication builds up or down).
Rather, "nine times larger" means multiplied by nine, and "nine times smaller" means divided by nine. This is basic and not particularly awkward, certainly not more so than e.g. positive/negative correlation, or many much more awkward and more common linguistic constructions, IMO.
If you have to edit out words (i.e. context) to argue a phrase doesn't make sense... I am not sure what mental model you have for natural language, exactly, but it certainly isn't a very robust one.
Conversely, 9x [filesize/natural number] is bigger. Every time. At least in the basic maths used by most people. There is no conversion into other units.
Therefore "9x smaller" when talking about a natural number like filesize is a nonsense statement in logic terms. If you strive for unambiguous phrasing - which is a significant part of the programming experience - this logical nonsense might well perturb you.
But english language is a flexible thing and if the phrase communicates your intent to your audience then that's fine by me.
Multiplying some scale by units per period makes sense and is both linguistically and mathematically sound.
If 9 is "9 times greater" than 1 then 1 must be "9 times smaller" than 9
It'd help if you read "9 times" with the operator which is what's being flipped instead of with the number
I don't see what makes it hard to understand.
if I say 'this Apple M5 chip is 3x faster' than this intel chip, it implies two things:
- the run time of most operations that runs on it is now reduced (so one quantity is smaller)
- but also: MORE WORK is being completed per unit of time compared to the intel chip (so this quantity is greater)
So yes, a greater quantity is being measured in the apple chip compared to the intel when you say apple is N times faster. i guess this a quirk with the word 'faster' - it actually measures two things, time and work performed per unit of time. the word smaller just measures size.
like, if I give a customer a cup of coffee one day, then give them a SMALLER cup of coffee the next day, for the same price, but declare "It's now 2X more space efficient!" i.e. it's now half the size, I'm certain the customer is gonna be pissed.