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English is weird

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Is it cold in here?:
I worked on avionics once and there was a box on a diagram labeled "error amplifier".

It's not as funny as it sounds. "Error" is in that context the technical term for the difference between where a control surface is commanded to be and where it currently is. Every time it has to move, there is an "error" measured.

oddtail:
The difference (or lack thereof) between "error" and "mistake" can vary wildly depending on context and how casual the use is.

But! I'm competent to explain the difference in one particular context, that is in linguistics.

A linguistic mistake is a slip-up that is one-time and holds no significance. It may be a careless misspelling, a slip of the tongue, generally - using language wrong that is no indication of actual language competence. One may or may not notice it, but when shown the mistake, the person who made it will be able to clearly see it.

A linguistic error is systematic - it's not an incidental imperfection, it's due to actually using language wrong. It's a repeatable mistake. The general assumption in linguistics is that language errors is what learners of a language do, due to imperfect grasp of the language's grammar - a native speaker doesn't make language errors by definition. As in - if you use language a certain way, that's your particular idiolect of that language, and is by definition correct (at least in the approach I've been taught in college - I don't know if mainstream consensus has shifted since I studied at university, but I doubt it did). If you use a foreign language, you're a non-native user, so your language intuition is based on learning the language and not acquiring it naturally, so you're reproducing a language that isn't natural for you. Therefore, you can make systematic errors.

I'm sure the mistake-error distinction can mean something else outside that specific context, and even when talking about language, it's probably not how it works when not using precise linguistic terminology (I think in casual speech, the two are pretty much interchangeable?). But thought giving that extra piece of info might possibly be useful.

Gyrre:
Sounds like it's a function application.

So it seems like errors occur while working within some sort of system. Whether it's a foreign language, a positioning system, mathematics, etc.

FreshScrod:
I think "error" is the more general one, and "mistake" is when it's done by someone. You can make a mistake, but your computer can't - those are errors. (I've also read that "bug" and "glitch" have a similar difference. I think it's that "glitch" is the symptom, and "bug" is the cause - but the first computer "bug" was a literal bug mucking up the works, so it would really be a glitch?) That's the way I use it, at least. I think then, when "mistake" is applicable, it's a different connotation if you just say "error" - I think "error" would then focus on the consequences, as they differ from how it should be, while "mistake" makes it more personal. I think in the specific case of a spelling error, unless I'm familiar with the process of how the text came to be, I can't really know if it was the author or the "printer" that caused the error. Actually, I first typed "made the error" for the previous sentence, but that looked wrong, so I think it's really that "error" denotes the effect, while "mistake" is the glitch in the human that is erroneous.
I also agree with oddtail's example. I'm starting to get the impression that "error" is also more abstract, while "mistake" is more tangible. Back with the spelling error - if I caused the spelling error, I use the word "mistake" in my mind, but if I see that something else caused it, like a glitch in the computer, then I use "error". Similarly, I don't know about how the error happened in the case of seeing someone else's writing having poor spelling, so I use "error" for that.

IICIH? I think the avionics one is because "err" originally meant "wander" so the "error" would be how much the flight has strayed from the precise course, which I understand is expected and natural in flight.

cybersmurf:
Is it possible "error" is more quantifiable? Since it's called "margin of error". Something in the likes of hair vs hairs (not singular vs plural, but the quantifiable amount of single hairs vs. the thing as a whole)

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