when people say "orders of magnitude" do they always mean base 10?
(i'm thinking of how decibels are a log scale sort of thing wrt power, where "orders of magnitude" used as a cliche probably does not mean what it would be read as.)
The wikipedia article was actually pretty interesting on this point. They suggest that 10 is commonly used, but other bases may be contextually relevant.
> An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10
I guess you could think of it like a _really_ low precision float or something.
I suspect the phrase is a cliche often used to sound scientific and sometimes by folks unaware, like how description of growth as “exponential” is a cliche used by non-mathematical discussion.
I agree with this. As a layman, I've always understood "orders of magnitude larger" to just mean "way too big" and "exponential" growth to imply "out of control".
x^2 and 2^x manifestly both involve exponents, so I think it's valid - outside math class - to call anything involving accelerating growth "exponential".
> when people say "orders of magnitude" do they always mean base 10?
Yes, and that has always bothered me just a little bit, given that there is nothing intrinsically special about base 10 and yet the phrase seems to suggest something fundamental.
No, 1 decibel is 10^1/10. Bels are multiplicative, not additive. You multiply 10^.1 by itself 10 times and you get 10^1. Similarly if you multiply x^1/2 by x^1/2 you get x.
That seems confusing. If I say my new service is orders of magnitude more efficient than previous services, I don’t mean any thing about scaling but current performance, and I wouldn’t say orders of magnitude if it was just twice as many calls/second/core, but more than ten, or really more than 30, halfway between ten and a hundred, logarithmically.
Something that scales geometrically might well have some giant constant so it isn’t useful until a specific performance regime.
(i'm thinking of how decibels are a log scale sort of thing wrt power, where "orders of magnitude" used as a cliche probably does not mean what it would be read as.)