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Comment by akoboldfrying | Hacker News Reader

I would say everyone understands that "quantum effects" refers to situations in which classical approximations break down.

Likewise when we say "numerical issues", it's understood that we're talking about situations in which the usual approximation of real numbers by floating point representations breaks down. "Disk corruption" doesn't necessarily mean anything is physically wrong with the disk, only that its contents have become inconsistent with the filesystem abstraction it normally supports, etc.

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The numerical version of this sin is

    typedef float real;

which promotes a similar confusion of concepts, even if the true meaning is understood by experts.

That said, I think the QM/not QM lingo from the molecular dynamics community is considerably worse because it stokes a common misunderstanding: that the universe runs on classical mechanics except in lasers, particle accelerators, and other "exotic circumstances." By contrast, nobody thinks that the universe runs on float32s except in lasers and spaceships where it runs on float64s. Where confusion does not exist, we do not need to fight it, but where it does, we should probably try.

>Likewise when we say "numerical issues", it's understood that we're talking about situations in which the usual approximation of real numbers by floating point representations breaks down.

Guys, try this in your desktop or mobile app calculator:

do square root of 2.

then subtract from it the result that you see on screen.

for me:

√2−1.41421356237

i get:

3.095048801E−12

i.e. not 0.

I discovered this on a physical Casio electronic calculator long back, and also verified it just now on a stock Android mobile calculator app.

what is your result, and interpretation of it?

It's just the difference between internal and displayed precision.

sqrt(2) ≈ 1.414213562373095048801

So if you type in sqrt(2) - 1.41421356237, you're just getting the next 10 digits after that.

      1.414213562373095048801
    - 1.41421356237
    _________________________
      0.000000000003095048801

= 3.095048801e12

yes, exactly :)

that's what i figured out when i first came across this, in school.

> what is your result, and interpretation of it?

that the square root of 2 is not 1.41421356237.

true, because the √2 is an irrational number.

but I was looking for an answer more along the lines that anamexis gave.

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