https://www.explainxkcd.com/wiki/api.php?action=feedcontributions&feedformat=atom&user=BrightVampexplain xkcd - User contributions [en]2026-06-17T21:59:05ZUser contributionsMediaWiki 1.30.0https://www.explainxkcd.com/wiki/index.php?title=2295:_Garbage_Math&diff=1908042295: Garbage Math2020-04-17T17:51:52Z<p>BrightVamp: Added information about possible statistical inspirations.</p>
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<div>{{comic<br />
| number = 2295<br />
| date = April 17, 2020<br />
| title = Garbage Math<br />
| image = garbage_math.png<br />
| titletext = 'Garbage In, Garbage Out' should not be taken to imply any sort of conservation law limiting the amount of garbage produced.<br />
}}<br />
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==Explanation==<br />
{{incomplete|Created by a ZILOG Z80. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}<br />
This comic explains the "garbage in, garbage out" concept using arithmetical expressions. Just like the comic says, if you get garbage in any part of your workflow, you get garbage as a result.<br />
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Some of these rules correspond to the rules of floating point arithmetic (https://en.wikipedia.org/wiki/Floating-point_arithmetic), while others may be inspired by the rules of propagation of uncertainty (https://en.wikipedia.org/wiki/Propagation_of_uncertainty#Example_formulae) where a "garbage" number would correspond to an estimate with a high degree of uncertainty, and the uncertainty of the result of arithmetic operations will tend to be dominated by the term with the highest uncertainty. The rule about N pieces of independent garbage reflects the central limit theorem (https://en.wikipedia.org/wiki/Central_limit_theorem) and how it predicts that the uncertainty (or standard error https://en.wikipedia.org/wiki/Standard_error) of an estimate will be reduced when independent estimates are averaged. <br />
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==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
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[A series of mathematical equations are written from top to bottom]<br />
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PRECISE NUMBER + PRECISE NUMBER = SLIGHTLY LESS PRECISE NUMBER<br />
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PRECISE NUMBER x PRECISE NUMBER = SLIGHTLY LESS PRECISE NUMBER<br />
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PRECISE NUMBER + GARBAGE = GARBAGE<br />
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PRECISE NUMBER x GARBAGE = GARBAGE<br />
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GARBAGE [inside square root symbol] = LESS BAD GARBAGE<br />
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(GARBAGE)2 [superscript '2' as exponentiation] = WORSE GARBAGE<br />
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1/N [Greek letter Sigma] (N PIECES OF STATISTICALLY INDEPENDENT GARBAGE) = BETTER GARBAGE<br />
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(PRECISE NUMBER)GARBAGE [superscript 'GARBAGE' as exponentiation] = MUCH WORSE GARBAGE<br />
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GARBAGE - GARBAGE = MUCH WORSE GARBAGE<br />
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PRECISE NUMBER<br />
___________________ = MUCH WORSE GARBAGE, POSSIBLE DIVISION BY ZERO<br />
(GARBAGE - GARBAGE) <br />
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GARBAGE x 0 = PRECISE NUMBER<br />
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{{comic discussion}}</div>BrightVamp