"Order of magnitude" is one of my linguistic pet peeves. I've seen it used referring to base 2, base 10, base 1000, and base 1024. What does it all mean? In base 2^(1/100), trebling is many, many orders of magnitude increase!
“Order of magnitude” is context-dependent, like a great many things in natural language. In the absence of any contrary context, it’ll mean a decimal order of magnitude in English. It will do you no good to rail against the inclusion of cultural context in resolving the meaning of language (and even its structural parsing!), because it’s so very widespread in English and I presume in every other natural language (though logical languages could potentially theoretically evade it).
Agreed, railing against language and cultural context is literally futile. Factoradic is the one true base. There, "order of magnitude" would depend not only upon (my very unique) cultural context but also the absolute magnitude involved (at the low end, "double" is an order of magnitude; then "triple", then "quadruple", etc).
I love these sorts of discussions. You learn things you’ve never heard of before. I can easily see how it works and how it’d be useful sometimes, but I’ve never come across it before. https://en.wikipedia.org/wiki/Mixed_radix is good related reading (including the concept of measuring time in this way; now that is something that we sometimes do in software, more or less).
I prefer to say “several times larger/greater” and it is even fewer syllables! “Order of magnitude” works better for convincing people to do something your way, though.
