{{comic
| number = 2295
| date = April 17, 2020
| title = Garbage Math
| image = garbage_math.png
| titletext = 'Garbage In, Garbage Out' should not be taken to imply any sort of conservation law limiting the amount of garbage produced.
}}

==Explanation==
{{incomplete|Created by a ZILOG Z80. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}
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.

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.

This comic is probably not COVID-19 related (though arguably it could be related to doing statistical analyses with the varying quality of data related to the disease), meaning that the 19 comic streak preceding this on topics relating to COVID-19 is probably broken.

This comic is about the propagation of errors in numerical analysis and statistics, but described in much more colloquial terms. Numbers with low precision are termed as "garbage" and numbers with high precision are termed as "precise numbers".

{| class="wikitable"
!Formula
!Explanation
|-
|Precise number + Precise number = Slightly less precise number
|If we know absolute error bars, then adding two precise numbers will at worst add the sizes of the two error bars. For example, if our precise numbers are 1 (±10-6) and 1 (±10-6), then our sum is 2 (±2·10-6). It is possible to lose a lot of relative precision, if the resultant sum is close to zero as a result of adding a number and then close to its inverse. This phenomenon is known as catastrophic cancellation. Therefore, it is likely that all numbers referred here are positive numbers, which does not exhibit this phenomenon.
|-
|Precise number × Precise number = Slightly less precise number
|Here, instead of absolute error, relative error will be added. For example, if our precise numbers are 1 (±10-6) and 1 (±10-6), then our product is 1 (±2·10-6).
|-
|Precise number + Garbage = Garbage
|If one of the numbers has a high absolute error, and the numbers being added are of comparable size, then this error will be propagated to the sum.
|-
|Precise number × Garbage = Garbage
|Likewise, if one of the numbers has a high relative error, then this error will be propagated to the sum. Here, this is independent of the sizes of the numbers.
|-
|<math>\sqrt{\text{Garbage}} = \text{Less bad garbage}</math>
| When a number is square rooted, its relative error will be halved.
|-
|Garbage2 = Worse garbage
|Likewise, when a number is squared, its relative error will be doubled. This is a corollary to multiplication adding relative errors.
|-
|<math>\frac{1}{N}\sum(\text{N pieces of statistically independent garbage}) = \text{Better garbage}</math>
|By aggregating many pieces of statistically independent observations (for instance, surveying many individuals), it is possible to reduce relative error. This is the basis of statistical sampling.
|-
|Precise numberGarbage = Much worse garbage
|The exponent is very sensitive to changes, which may also magnify the effect based on the magnitude of the precise number.
|-
|Garbage - Garbage = Much worse garbage
|This line involves catastrophic cancellation. If both pieces of garbage are about the same (e.g. if their error bars overlap), then it is possible that the answer is positive, zero, or negative.
|-
|<math>\frac{\text{Precise number}}{\text{Garbage}-\text{Garbage}}</math>=Much worse garbage, possible division by zero
|Indeed, as with above, if error bars overlap then we might end up dividing by zero.
|-
|Garbage × 0 = Precise number
|Multiplying anything by 0 results in 0, an extremely precise number in the sense that it has no error whatsoever since we supply the 0 ourselves. This is equivalent to discarding garbage data from a statistical analysis.

The titletext refers to the computer science maxim of Garbage in, garbage out, which states that even if some code accurately does what it is supposed to do, supplying incorrect data will result in incorrect results. 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.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

[A series of mathematical equations are written from top to bottom]

PRECISE NUMBER + PRECISE NUMBER = SLIGHTLY LESS PRECISE NUMBER

PRECISE NUMBER x PRECISE NUMBER = SLIGHTLY LESS PRECISE NUMBER

PRECISE NUMBER + GARBAGE = GARBAGE

PRECISE NUMBER x GARBAGE = GARBAGE

GARBAGE [inside square root symbol] = LESS BAD GARBAGE

(GARBAGE)2 [superscript '2' as exponentiation] = WORSE GARBAGE

1/N [Greek letter Sigma] (N PIECES OF STATISTICALLY INDEPENDENT GARBAGE) = BETTER GARBAGE

(PRECISE NUMBER)GARBAGE [superscript 'GARBAGE' as exponentiation] = MUCH WORSE GARBAGE

GARBAGE - GARBAGE = MUCH WORSE GARBAGE

PRECISE NUMBER

_________________ = MUCH WORSE GARBAGE, POSSIBLE DIVISION BY ZERO

GARBAGE - GARBAGE

GARBAGE x 0 = PRECISE NUMBER

{{comic discussion}}

1917: How to Make Friends

2017-12-10T04:34:50Z

172.69.22.152: /* Explanation */

{{comic
| number = 1917
| date = November 17, 2017
| title = How to Make Friends
| image = how_to_make_friends.png
| titletext = No, wait, come back! I want to be friends at you!
}}

==Explanation==
This comic follows an example interaction, purportedly showing how to make friends. We see [[Cueball]]'s strategy for making friends. It does incorporate various points of advice for building friendships, which are completely sound in the abstract. But it's clearly not helping him -- he's out of sync with the interaction context and makes bigger social gaffes by following the abstract advice. Escalating awkwardness ensues.

It starts out with a common way of making friends or interacting with friends, hanging out over a meal. However, Cueball suggests doing so with awkwardly literal phrasing; whereas most people use expressions such as “have lunch” or “grab a bite to eat”, Cueball explicitly invites Hairy to “eat food”. The fact that he feels the need to clarify that they’ll be eating food, as opposed to any other orally consumable items, indicates his lack of confidence to clearly communicate his intentions.

Before Hairy can even respond, Cueball then says that they could instead “sit together and talk without eating.” Although this is indeed another common way to make friends, it’s kind of an odd way to phrase it, especially since he didn’t even give Hairy a chance to reply to his initial suggestion. Cueball then says he doesn’t need to eat (meaning not ''right now'', especially as a prerequisite to talking), but he immediately feels compelled to clarify that he ''does'' need to eat (meaning ''in general''), and again it’s weird that he clarified, as his original wording probably would have been understood. He then awkwardly remarks about how he can eat later if Hairy would rather just talk. The overall implication is that Cueball’s awkwardness and over-explanation would be off-putting to a typical person.

This is apparently a situation that Randall has encountered before, and he apologizes for trying to offer advice.

The title text says Cueball wants to be friends ''at'' Hairy, rather than ''with'' him, which isn’t how friendship usually works. “At” implies that Cueball considers being friends to be a unilateral action that he needs to direct towards Hairy, like “smiling at” or “pointing at”, and does not understand that it is typically a mutual activity of building a relationship, which would be indicated by being friends ''with'' him. “At” can even carry a degree of animosity (compare: [https://en.wikiquote.org/wiki/The_Hitchhiker's_Guide_to_the_Galaxy#Chapter_17_2 “he just phoned up to wash his head at us”]).

==Transcript==

:[First panel with words:]
:''Presenting:''

:How to make friends

:[Second panel with Cueball and Hairy facing each other:]
:Cueball: Want to go eat food together?
:Cueball: We could also sit together and talk without eating. I don't need to eat. I mean, I do need to eat. But if you don't want to eat then we can just talk. I can eat later.

:[Third panel with words:]
:''Okay''

:It turns out I still haven't figured out how to do this.

:''Sorry''

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Hairy]]