Garbage Math
Garbage Math
[A series of mathematical equations are written from top to bottom]
Precise number + Precise number = Slightly less precise number
Precise number × Precise number = Slightly less precise number
Precise number + Garbage = Garbage
Precise number × Garbage = Garbage
√ Garbage = Less bad garbage
Garbage² = Worse garbage
1/N Σ (N pieces of statistically independent garbage) = Better garbage
(Precise number) Garbage = Much worse garbage
Garbage – Garbage = Much worse garbage
Precise number / ( Garbage – Garbage ) = Much worse garbage, possible division by zero
Garbage × 0 = Precise number

This comic illustrates the " garbage in, garbage out " concept using mathematical expressions. It shows how, if you have garbage as inputs to your calculations, then you will likely get garbage as a result, except when you multiply by zero, which eliminates all uncertainty of the result.
The propagation of errors in arithmetic , other mathematical operations , and statistics is described in colloquial terms. Numbers with low precision are termed garbage, while numbers with high precision are called precise. The table below quantifies the change in precision from the operands to their result in terms of their variance , represented by σ, the Greek lowercase letter sigma, equal to the standard deviation , or the square root of the variance. Variance or standard deviation are common specifications of uncertainty (as an alternative to, for example, a tolerance interval .)
The accuracy and precision of mathematical operations correspond to the rules of propagation of uncertainty , where a "garbage" number would correspond to an estimate with a high degree of uncertainty, and a precise number has low uncertainty. The uncertainty of the result of such operations will usually correspond to the term with the highest uncertainty. The rule about N pieces of independent garbage used to calculate an arithmetic mean reflects how the central limit theorem predicts that the uncertainty (or standard error ) of an estimate will be reduced when independent estimates are averaged.
The title text refers to the computer science maxim of "garbage in, garbage out," which states that when it comes to computer code, supplying incorrect initial data will produce incorrect results, even if the code itself accurately does what it is supposed to do. As we can see above, however, when plugging data into mathematical formulas, this can possibly magnify the error of our input data, though there are ways to reduce this error (such as aggregating data). Therefore, the quantity of garbage is not necessarily conserved , in contrast to other scientific quantities like energy and momentum that are always conserved. Alternatively, this could be take as a pun on environmental conservation efforts, which can often involve recycling one's trash. However, the computer science maxim of "garbage in, garbage out," has nothing to do with actual garbage.
[A series of mathematical equations are written from top to bottom]
Precise number + Precise number = Slightly less precise number
Precise number × Precise number = Slightly less precise number
Precise number + Garbage = Garbage
Precise number × Garbage = Garbage
√ Garbage = Less bad garbage
Garbage² = Worse garbage
1/N Σ (N pieces of statistically independent garbage) = Better garbage
(Precise number) Garbage = Much worse garbage
Garbage – Garbage = Much worse garbage
Precise number / ( Garbage – Garbage ) = Much worse garbage, possible division by zero
Garbage × 0 = Precise number
