explain xkcd - User contributions [en]

2295: Garbage Math

2020-04-20T07:50:39Z

162.158.255.64: /* Explanation */ missing paren

{{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 illustrates the "{{w|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 {{w|arithmetic}}, other {{w|mathematical operations}}, and {{w|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 {{w|variance}}, represented by σ, the Greek lowercase letter sigma, equal to the {{w|standard deviation}}, or the square root of the variance. Variance or standard deviation are common specifications of precision (as an alternative to, for example, a {{w|tolerance interval}}.)

The {{w|accuracy and precision}} of mathematical operations correspond to the rules of {{w|Propagation_of_uncertainty#Example_formulae|propagation of uncertainty}}, where a "garbage" number would correspond to an estimate with a high degree of 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 {{w|arithmetic mean}} reflects how the {{w|central limit theorem}} predicts that the uncertainty (or {{w|standard error}}) of an estimate will be reduced when independent estimates are averaged.

{| class="wikitable"
!Formula as shown
!Resulting uncertainty
!Explanation
|-
|Precise number + Precise number = Slightly less precise number
|<math>\mathop\sigma(X+Y)=\sqrt{\mathop\sigma(X)^2+\mathop\sigma(Y)^2}</math>
|{{Nowrap|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 to its approximate negation, a phenomenon known as {{w|catastrophic cancellation}}. Therefore, both of the numbers must be positive for the stated assertion to be true.
|-
|Precise number × Precise number = Slightly less precise number
|<math>\mathop\sigma(X\times Y)=</math> <math>\sqrt{\mathop\sigma(X)\times Y^2+\mathop\sigma(Y)\times X^2}</math>
|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
|<math>\mathop\sigma(X+Y)=\sqrt{\mathop\sigma(X)^2+\mathop\sigma(Y)^2}</math>
|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
|<math>\mathop\sigma(X\times Y)=</math> <math>\sqrt{\mathop\sigma(X)\times Y^2+\mathop\sigma(Y)\times X^2}</math>
|Likewise, if one of the numbers has a high relative error, then this error will be propagated to the product. Here, this is independent of the sizes of the numbers.
|-
|√Garbage = Less bad garbage
|<math>\mathop\sigma(\sqrt X)=\frac{\mathop\sigma(X)}{2\times\sqrt X} </math>
| When the square root of a number is computed, its relative error will be halved. Depending on the application, this might not be all that much ''better'', but it's at least ''less bad''.
|-
|Garbage2 = Worse garbage
|<math>\mathop\sigma(X^2)=2\times X\times\mathop\sigma(X)</math>
|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(</math>N pieces of statistically independent garbage<math>)</math> = Better garbage
|<math>{\sigma}_\bar{x}\ = \frac{\sigma_x}{\sqrt{N}}</math>
|By aggregating many pieces of statistically independent observations (for instance, surveying many individuals), it is possible to reduce relative error to the {{w|Standard_error#Standard_error_of_the_mean|standard error of the mean}}. This is the basis of statistical sampling and the {{w|central limit theorem}}.
|-
|Precise numberGarbage = Much worse garbage
|<math>\mathop\sigma(b^X)=b^{2\times X}\times\mathop{\mathrm{ln}}b\times\sigma(X)</math>
|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
|<math>\mathop\sigma(X-Y)=\sqrt{\mathop\sigma(X)^2+\mathop\sigma(Y)^2}</math>
|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
|<math>\mathop\sigma(\frac{a}{X-Y})=</math> <math>|\frac a{X-Y}|\times\sqrt{\mathop\sigma(X)^2+\mathop\sigma(Y)^2}</math>
|Indeed, as with above, if error bars overlap then we might end up dividing by zero.
|-
|Garbage × 0 = Precise number
|<math>\mathop\sigma(0)=0</math>
|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 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.

==Transcript==

[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

{{comic discussion}}
[[Category:Math]]

Talk:2295: Garbage Math

2020-04-20T07:48:01Z

162.158.255.64: question

== Inclusion in Series ==
This is not a Covid19 comic. One could think that this is a comment on the difficulties of modeling the corona virus outbreak, but since discussions of exponential functions are only a small part in the comic I believe it is just a general comment on floating point arithmetic mixed in with statistical considerations. --[[Special:Contributions/108.162.229.242|108.162.229.242]] 17:28, 17 April 2020 (UTC)
:I disagree that this is not a COVID-19 comic. I also believe the one about visualizing large numbers was COVID-19 related. On the other hand, I like the idea that Randall might produce exactly 19 comics related to SARS CoViD 2019, so I'm prepared to concede the point for the sake of arbitrary numerological appeal.
:[[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 18:42, 17 April 2020 (UTC)
::I think Exa-Exabyte was a real stretch (the virus doesn't even have DNA), but there is a tenuous link so whatever. The idea that ''this'' comic is related, on the other hand, stretches past the breaking point. There's hardly anything that can't be linked to global events if we try hard enough, but that doesn't mean there's an actual link. Sometimes a comic about garbage math is just a comic about garbage math. [[Special:Contributions/172.69.71.58|172.69.71.58]] 19:33, 17 April 2020 (UTC)
:::I think this one's much more likely to be a coronavirus comic than Exa-Exabyte was. There's an awful lot of COVID data, much of it either very imprecise or outright garbage; and the comic directly before this one ([[2294]]) involved bad modeling of said COVID data, so clearly COVID data (and its limitations) is something Randall's currently thinking of and drawing comics about. [[User:Pelosujamo|Pelosujamo]] ([[User talk:Pelosujamo|talk]]) 20:25, 17 April 2020 (UTC)
::::Exa-Exabyte was centered around biology, which gives reason to believe it was covid19 related. This one seems much more uncertain. Any conclusion that it is related is based on garbage. Jokes aside, It seems like much more of a stretch to me. Randall thinking in those terms is a reasonable argument, but personally I am going to assume this is the chain breaker unless a direct reference is made in the next couple comics since ending at 19 is would be appropriate. [[Special:Contributions/172.69.70.209|172.69.70.209]]
:: While this comic has no ''direct'' reference to Covid-19 it does appear that the math might be related. At this point we can't know if the series has ended. As such I've edited the paragraph in the explanation to identify the known ambiguities. And now I realize I've made an explanatory paragraph about "knowledge error bars" in the explanation of a comic about numerical error bars.[[User:Iggynelix|Iggynelix]] ([[User talk:Iggynelix|talk]]) 14:42, 18 April 2020 (UTC)
:::No. The reason it appears the math might be related is ''because the math relates to everything, everywhere''. That's not enough of a connection. During this pandemic, there will be a lot of comics related to the coronavirus, many of them in a row, but that doesn't mean that every comic that could be tangentially related if you squint just right should qualify as a COVID-19 comic (I ''still'' think Exa-Exabyte doesn't). There needs to be a real link, because just about ''anything'' could be twisted into a relation if you try hard enough. As a test, I hit [[Special:Random]] and got [[346: Diet Coke+Mentos]]. Wouldn't you know, that's a coronavirus comic! The father, you see, actually had COVID-19 and died, but Diet Coke and Mentos has brought him back! No. The line should be drawn here. The streak has ended. [[Special:Contributions/172.69.68.197|172.69.68.197]] 17:02, 18 April 2020 (UTC)
::::I agree this is not a serious contender for inclusion as a COVID comic. Although I'm pretty sure Randall has input to COVID19 models as garbage on his mind. But there is nothing in this comic that suggest this math be used on a pandemic. The exa byte is a different story as it is about how much of biology we cannot know or control in the midst of a lot of comics about some new biology we do not control. I do not expect that this will end the covid19 series, but I will consent that even if the next comic is a clear corona comic, it will no longer be an unbroken streak. Anyway the real streak ended at the end of March with the late April Fool's comic. I also do not at all think that the coke mentos could be seen as a COVID19 comic, that is just bulls**t trying to prove a point that I believe you fail completely. I also tried random comic (I like the idea) and found [[1208: Footnote Labyrinths]]. It is a scientific paper (with nested footnotes) and given science, we could say it was about science about Corona. Naah. But for the same reason this comic should not be considered corona. --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 20:53, 18 April 2020 (UTC)

:::::I am pretty sure this IS related. Right now, everybody and his grandmother is staring at the Johns Hopkins Coronavirus numbers for different countries. Entire newspaper articles are written about these numbers and about why one country is apparently faring better than the other and what this means. The numbers are made into fancy graphics. People use these numbers to calculate fatality rates and cure rates. Politicians might even use these numbers to make decisions.
:::::And all this even though everybody KNOWS that the numbers cannot really be compared from one country to the other, because testing prerequisites vary, testing availability varies, testing procedures vary, criteria used to include a death as a coronavirus death vary. The sources of the numbers are very different and might not always be reliable. [Apparently, they include local language newspapers, website and even social media accounts. How many people DOES the Johns Hopkins University have to track all these sources reliably, worldwide, in local languages?] And not to forget some countries probably are downright lying.
:::::And still, people are comparing. I've read articles where the author admits the numbers are probably garbage in one sentence and then STILL goes on to calculate fatality rates from them in the next sentence. So, most PROBABLY related.

::::::I challenge you to find a comic in the archive that can't be twisted to say it's related to COVID-19. At this point people are finding connections in the same way that people analyze "the curtain is blue". [[Special:Contributions/108.162.245.26|108.162.245.26]] 22:06, 19 April 2020 (UTC)
--[[Special:Contributions/141.101.69.153|141.101.69.153]] 21:53, 19 April 2020 (UTC)

This comic very much reminds me of this article: [https://www.realclearmarkets.com/articles/2020/04/17/its_decidedly_not_the_math_its_always_people_489344.html
It's Decidedly Not the Math. It's Always People] So much so that my first thought was that the comic was inspired by it, though of course I can't prove it.[[User:BrianZ|BrianZ]] ([[User talk:BrianZ|talk]]) 00:52, 20 April 2020 (UTC)

== Math and Error bars ==

Well this is surprising came here thinking I understood it just to see what the discussion looked like. Ended up learning something new. I was able to understand intuitively the comic. But this is my first exposure to actually doing math on the error bars. I think I was supposed to do that in college but I don't remember anyone ever explaining how it should work. --[[Special:Contributions/162.158.63.208|162.158.63.208]] 18:14, 17 April 2020 (UTC)

In recent days, there have been a number of math "quizzes" in this same type of format, albeit generally with only addition and maybe multiplication, appearing on Facebook. Should the explanation include a reference to this as a possible contributing reason for Randall's comic? One could also argue that those quizzes have been appearing on Facebook as a way to spend/waste time during the coronavirus pandemic lock-down, making he comic at least tangentially related to Covid19 LIES.
:: Unsigned vandalism? /\ [https://www.explainxkcd.com/wiki/index.php?title=Talk:2295:_Garbage_Math&diff=190866&oldid=190856 change history] @user Please feel free to move your discussion to an appropriate forum and remove both the edit and this comment at such time. [[User:Iggynelix|Iggynelix]] ([[User talk:Iggynelix|talk]])

What's the difference between relative error and absolute error? I don't understand these terms. Maybe add?
: Absolute error is the amount of uncertainty in a value measured as a given number. e.g. 5.7 ± 1.2 means that actual value lies somewhere between 5.7 - 1.2 and 5.7 + 1.2 = 4.5 to 6.9. If you change the 5.7 to another value, you still get the same absolute difference of maximum and minimum values. Relative error depends on the value you are comparing to. e.g. 5.7 ± 10% would be between 5.7 - 0.57 and 5.7 + 0.57 = 5.13 to 6.27. The absolute difference of maximum and minimum would change if the main number changes. e.g. 11.3 ± 10% would be between 10.17 and 12.43, which has a greater absolute difference of maximum and minimum than the previous example. [[User:Nutster|Nutster]] ([[User talk:Nutster|talk]]) 01:54, 18 April 2020 (UTC)

Are all of these equations consistent with garbage = infinity?
: Unfortunately, as written, these equations would not make sense by defining Garbage as an infinity. Infinity is not a number you can count to or measure in between integers. Infinity is the idea of unending-ness. Trying to use infinity as if it a finite number yields all sorts of invalid results. In this case Garbage is defined as an arbitrary finite number with a large amount of uncertainty in its value. [[User:Nutster|Nutster]] ([[User talk:Nutster|talk]]) 01:40, 18 April 2020 (UTC)
::: That's a pretty good definition of 'garbage' in ''any'' case, plus or minus 10%. ( See also [https://www.weforum.org/agenda/2017/06/landfill-mining-recycling-eurelco/ valuable garbage]) [[User:Iggynelix|Iggynelix]] ([[User talk:Iggynelix|talk]]) 14:19, 18 April 2020 (UTC)

Would the summation divided by ''n'' just give you the arithmatic mean of the data set? [[User:Nutster|Nutster]] ([[User talk:Nutster|talk]]) 01:55, 18 April 2020 (UTC)
:Pretty much, but the point is probably more that (without consistent bias across the set, just 'random' errors for each item) it suppresses the degree of garbagicity as outliers are increasingly nullified by the greater number of more competently accurate values and (if it's a symmetric error) opposing outliers. [[Special:Contributions/162.158.34.222|162.158.34.222]] 09:29, 18 April 2020 (UTC)

The statement that NaN^0 isn't fully justified and I'm not clear it belongs. [[User:Djbrasier|Djbrasier]] ([[User talk:Djbrasier|talk]]) 18:46, 18 April 2020 (UTC)
: I agree... It also isn't evident to me that this comic has anything to do with floating-point math, which is the only thing that could (even slimly) justify its inclusion. This is about statistics, not programming. --[[Special:Contributions/108.162.215.12|108.162.215.12]] 05:25, 19 April 2020 (UTC)

I'm concerned that, with "Precise Number" there's the usual confusion between Accuracy and Precision (''edit: and of course Resolution, too!''). A precise number can still be utter garbage, as 84.7489327(646475)% of all mathematicians could tell you. [[Special:Contributions/162.158.111.241|162.158.111.241]] 13:59, 19 April 2020 (UTC)
:The table of formulae for the propagation of variance σ addresses that aspect. You can't know the accuracy of a result without knowing the precision of its calculation, and while reducing precision always reduces accuracy, it's not the other way around. But precision is inherent in the representation and operations, while accuracy is secondary when you aren't discussing the initial measurements of the inputs, so I think the terminology is correct.
:By the way, shout out to [https://www.explainxkcd.com/wiki/index.php?title=2295%3A_Garbage_Math&type=revision&diff=190882&oldid=190870 172.68.51.124] for filling out all but one of those table entries. I wonder where they looked them up. I'm guessing a ''CRC Handbook'' left over from High School chemistry or some such? Anyway, good job! This really looks classy now that it's been cleaned up a bit. [[Special:Contributions/162.158.255.64|162.158.255.64]] 06:45, 20 April 2020 (UTC)

Could someone please double check that the given uncertainty formula for "Precise number / ( Garbage – Garbage )" at the second to the bottom is correct? I'm not sure it properly accommodates the uncertainty of the numerator. [[Special:Contributions/162.158.255.64|162.158.255.64]] 07:48, 20 April 2020 (UTC)

2295: Garbage Math

2020-04-20T07:45:06Z

162.158.255.64: /* Explanation */ typos

{{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 illustrates the "{{w|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 {{w|arithmetic}}, other {{w|mathematical operations}}, and {{w|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 {{w|variance}}, represented by σ, the Greek lowercase letter sigma, equal to the {{w|standard deviation}}, or the square root of the variance. Variance or standard deviation are common specifications of precision (as an alternative to, for example, a {{w|tolerance interval}}.

The {{w|accuracy and precision}} of mathematical operations correspond to the rules of {{w|Propagation_of_uncertainty#Example_formulae|propagation of uncertainty}}, where a "garbage" number would correspond to an estimate with a high degree of 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 {{w|arithmetic mean}} reflects how the {{w|central limit theorem}} predicts that the uncertainty (or {{w|standard error}}) of an estimate will be reduced when independent estimates are averaged.

{| class="wikitable"
!Formula as shown
!Resulting uncertainty
!Explanation
|-
|Precise number + Precise number = Slightly less precise number
|<math>\mathop\sigma(X+Y)=\sqrt{\mathop\sigma(X)^2+\mathop\sigma(Y)^2}</math>
|{{Nowrap|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 to its approximate negation, a phenomenon known as {{w|catastrophic cancellation}}. Therefore, both of the numbers must be positive for the stated assertion to be true.
|-
|Precise number × Precise number = Slightly less precise number
|<math>\mathop\sigma(X\times Y)=</math> <math>\sqrt{\mathop\sigma(X)\times Y^2+\mathop\sigma(Y)\times X^2}</math>
|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
|<math>\mathop\sigma(X+Y)=\sqrt{\mathop\sigma(X)^2+\mathop\sigma(Y)^2}</math>
|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
|<math>\mathop\sigma(X\times Y)=</math> <math>\sqrt{\mathop\sigma(X)\times Y^2+\mathop\sigma(Y)\times X^2}</math>
|Likewise, if one of the numbers has a high relative error, then this error will be propagated to the product. Here, this is independent of the sizes of the numbers.
|-
|√Garbage = Less bad garbage
|<math>\mathop\sigma(\sqrt X)=\frac{\mathop\sigma(X)}{2\times\sqrt X} </math>
| When the square root of a number is computed, its relative error will be halved. Depending on the application, this might not be all that much ''better'', but it's at least ''less bad''.
|-
|Garbage2 = Worse garbage
|<math>\mathop\sigma(X^2)=2\times X\times\mathop\sigma(X)</math>
|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(</math>N pieces of statistically independent garbage<math>)</math> = Better garbage
|<math>{\sigma}_\bar{x}\ = \frac{\sigma_x}{\sqrt{N}}</math>
|By aggregating many pieces of statistically independent observations (for instance, surveying many individuals), it is possible to reduce relative error to the {{w|Standard_error#Standard_error_of_the_mean|standard error of the mean}}. This is the basis of statistical sampling and the {{w|central limit theorem}}.
|-
|Precise numberGarbage = Much worse garbage
|<math>\mathop\sigma(b^X)=b^{2\times X}\times\mathop{\mathrm{ln}}b\times\sigma(X)</math>
|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
|<math>\mathop\sigma(X-Y)=\sqrt{\mathop\sigma(X)^2+\mathop\sigma(Y)^2}</math>
|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
|<math>\mathop\sigma(\frac{a}{X-Y})=</math> <math>|\frac a{X-Y}|\times\sqrt{\mathop\sigma(X)^2+\mathop\sigma(Y)^2}</math>
|Indeed, as with above, if error bars overlap then we might end up dividing by zero.
|-
|Garbage × 0 = Precise number
|<math>\mathop\sigma(0)=0</math>
|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 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.

==Transcript==

[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

{{comic discussion}}
[[Category:Math]]

2295: Garbage Math

2020-04-20T07:40:55Z

162.158.255.64: /* Explanation */ floating point has nothing to do with any of these; try to explain better; swap paragraph order

{{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 illustrates the "{{w|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 {{w|arithmetic}}, other {{w|mathematical operations}}, and {{w|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 {{w|variance}}, represented by σ, the Greek lowercase letter sigma, equal to the {{w|standard deviation}}, or the square root of the variance. Variance or standard deviation are common specifications of precision (as an alternative to, for example, a {{w|tolerance interval}}.

The {{w|accuracy and precision}} of mathematical operations correspond to the rules of {{w|Propagation_of_uncertainty#Example_formulae|propagation of uncertainty}} where a "garbage" number would correspond to an estimate with a high degree of 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 compete an {{w|arithmetic mean}} reflects how the {{w|central limit theorem}} predicts that the uncertainty (or {{w|standard error}}) of an estimate will be reduced when independent estimates are averaged.

{| class="wikitable"
!Formula as shown
!Resulting uncertainty
!Explanation
|-
|Precise number + Precise number = Slightly less precise number
|<math>\mathop\sigma(X+Y)=\sqrt{\mathop\sigma(X)^2+\mathop\sigma(Y)^2}</math>
|{{Nowrap|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 to its approximate negation, a phenomenon known as {{w|catastrophic cancellation}}. Therefore, both of the numbers must be positive for the stated assertion to be true.
|-
|Precise number × Precise number = Slightly less precise number
|<math>\mathop\sigma(X\times Y)=</math> <math>\sqrt{\mathop\sigma(X)\times Y^2+\mathop\sigma(Y)\times X^2}</math>
|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
|<math>\mathop\sigma(X+Y)=\sqrt{\mathop\sigma(X)^2+\mathop\sigma(Y)^2}</math>
|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
|<math>\mathop\sigma(X\times Y)=</math> <math>\sqrt{\mathop\sigma(X)\times Y^2+\mathop\sigma(Y)\times X^2}</math>
|Likewise, if one of the numbers has a high relative error, then this error will be propagated to the product. Here, this is independent of the sizes of the numbers.
|-
|√Garbage = Less bad garbage
|<math>\mathop\sigma(\sqrt X)=\frac{\mathop\sigma(X)}{2\times\sqrt X} </math>
| When the square root of a number is computed, its relative error will be halved. Depending on the application, this might not be all that much ''better'', but it's at least ''less bad''.
|-
|Garbage2 = Worse garbage
|<math>\mathop\sigma(X^2)=2\times X\times\mathop\sigma(X)</math>
|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(</math>N pieces of statistically independent garbage<math>)</math> = Better garbage
|<math>{\sigma}_\bar{x}\ = \frac{\sigma_x}{\sqrt{N}}</math>
|By aggregating many pieces of statistically independent observations (for instance, surveying many individuals), it is possible to reduce relative error to the {{w|Standard_error#Standard_error_of_the_mean|standard error of the mean}}. This is the basis of statistical sampling and the {{w|central limit theorem}}.
|-
|Precise numberGarbage = Much worse garbage
|<math>\mathop\sigma(b^X)=b^{2\times X}\times\mathop{\mathrm{ln}}b\times\sigma(X)</math>
|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
|<math>\mathop\sigma(X-Y)=\sqrt{\mathop\sigma(X)^2+\mathop\sigma(Y)^2}</math>
|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
|<math>\mathop\sigma(\frac{a}{X-Y})=</math> <math>|\frac a{X-Y}|\times\sqrt{\mathop\sigma(X)^2+\mathop\sigma(Y)^2}</math>
|Indeed, as with above, if error bars overlap then we might end up dividing by zero.
|-
|Garbage × 0 = Precise number
|<math>\mathop\sigma(0)=0</math>
|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 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.

==Transcript==

[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

{{comic discussion}}
[[Category:Math]]

Talk:2295: Garbage Math

2020-04-20T06:49:55Z

162.158.255.64: /* Math and Error bars */ oops take two

Talk:2295: Garbage Math

2020-04-20T06:48:44Z

162.158.255.64: /* Math and Error bars */ oops same editor

== Inclusion in Series ==
This is not a Covid19 comic. One could think that this is a comment on the difficulties of modeling the corona virus outbreak, but since discussions of exponential functions are only a small part in the comic I believe it is just a general comment on floating point arithmetic mixed in with statistical considerations. --[[Special:Contributions/108.162.229.242|108.162.229.242]] 17:28, 17 April 2020 (UTC)
:I disagree that this is not a COVID-19 comic. I also believe the one about visualizing large numbers was COVID-19 related. On the other hand, I like the idea that Randall might produce exactly 19 comics related to SARS CoViD 2019, so I'm prepared to concede the point for the sake of arbitrary numerological appeal.
:[[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 18:42, 17 April 2020 (UTC)
::I think Exa-Exabyte was a real stretch (the virus doesn't even have DNA), but there is a tenuous link so whatever. The idea that ''this'' comic is related, on the other hand, stretches past the breaking point. There's hardly anything that can't be linked to global events if we try hard enough, but that doesn't mean there's an actual link. Sometimes a comic about garbage math is just a comic about garbage math. [[Special:Contributions/172.69.71.58|172.69.71.58]] 19:33, 17 April 2020 (UTC)
:::I think this one's much more likely to be a coronavirus comic than Exa-Exabyte was. There's an awful lot of COVID data, much of it either very imprecise or outright garbage; and the comic directly before this one ([[2294]]) involved bad modeling of said COVID data, so clearly COVID data (and its limitations) is something Randall's currently thinking of and drawing comics about. [[User:Pelosujamo|Pelosujamo]] ([[User talk:Pelosujamo|talk]]) 20:25, 17 April 2020 (UTC)
::::Exa-Exabyte was centered around biology, which gives reason to believe it was covid19 related. This one seems much more uncertain. Any conclusion that it is related is based on garbage. Jokes aside, It seems like much more of a stretch to me. Randall thinking in those terms is a reasonable argument, but personally I am going to assume this is the chain breaker unless a direct reference is made in the next couple comics since ending at 19 is would be appropriate. [[Special:Contributions/172.69.70.209|172.69.70.209]]
:: While this comic has no ''direct'' reference to Covid-19 it does appear that the math might be related. At this point we can't know if the series has ended. As such I've edited the paragraph in the explanation to identify the known ambiguities. And now I realize I've made an explanatory paragraph about "knowledge error bars" in the explanation of a comic about numerical error bars.[[User:Iggynelix|Iggynelix]] ([[User talk:Iggynelix|talk]]) 14:42, 18 April 2020 (UTC)
:::No. The reason it appears the math might be related is ''because the math relates to everything, everywhere''. That's not enough of a connection. During this pandemic, there will be a lot of comics related to the coronavirus, many of them in a row, but that doesn't mean that every comic that could be tangentially related if you squint just right should qualify as a COVID-19 comic (I ''still'' think Exa-Exabyte doesn't). There needs to be a real link, because just about ''anything'' could be twisted into a relation if you try hard enough. As a test, I hit [[Special:Random]] and got [[346: Diet Coke+Mentos]]. Wouldn't you know, that's a coronavirus comic! The father, you see, actually had COVID-19 and died, but Diet Coke and Mentos has brought him back! No. The line should be drawn here. The streak has ended. [[Special:Contributions/172.69.68.197|172.69.68.197]] 17:02, 18 April 2020 (UTC)
::::I agree this is not a serious contender for inclusion as a COVID comic. Although I'm pretty sure Randall has input to COVID19 models as garbage on his mind. But there is nothing in this comic that suggest this math be used on a pandemic. The exa byte is a different story as it is about how much of biology we cannot know or control in the midst of a lot of comics about some new biology we do not control. I do not expect that this will end the covid19 series, but I will consent that even if the next comic is a clear corona comic, it will no longer be an unbroken streak. Anyway the real streak ended at the end of March with the late April Fool's comic. I also do not at all think that the coke mentos could be seen as a COVID19 comic, that is just bulls**t trying to prove a point that I believe you fail completely. I also tried random comic (I like the idea) and found [[1208: Footnote Labyrinths]]. It is a scientific paper (with nested footnotes) and given science, we could say it was about science about Corona. Naah. But for the same reason this comic should not be considered corona. --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 20:53, 18 April 2020 (UTC)

:::::I am pretty sure this IS related. Right now, everybody and his grandmother is staring at the Johns Hopkins Coronavirus numbers for different countries. Entire newspaper articles are written about these numbers and about why one country is apparently faring better than the other and what this means. The numbers are made into fancy graphics. People use these numbers to calculate fatality rates and cure rates. Politicians might even use these numbers to make decisions.
:::::And all this even though everybody KNOWS that the numbers cannot really be compared from one country to the other, because testing prerequisites vary, testing availability varies, testing procedures vary, criteria used to include a death as a coronavirus death vary. The sources of the numbers are very different and might not always be reliable. [Apparently, they include local language newspapers, website and even social media accounts. How many people DOES the Johns Hopkins University have to track all these sources reliably, worldwide, in local languages?] And not to forget some countries probably are downright lying.
:::::And still, people are comparing. I've read articles where the author admits the numbers are probably garbage in one sentence and then STILL goes on to calculate fatality rates from them in the next sentence. So, most PROBABLY related.

::::::I challenge you to find a comic in the archive that can't be twisted to say it's related to COVID-19. At this point people are finding connections in the same way that people analyze "the curtain is blue". [[Special:Contributions/108.162.245.26|108.162.245.26]] 22:06, 19 April 2020 (UTC)
--[[Special:Contributions/141.101.69.153|141.101.69.153]] 21:53, 19 April 2020 (UTC)

This comic very much reminds me of this article: [https://www.realclearmarkets.com/articles/2020/04/17/its_decidedly_not_the_math_its_always_people_489344.html
It's Decidedly Not the Math. It's Always People] So much so that my first thought was that the comic was inspired by it, though of course I can't prove it.[[User:BrianZ|BrianZ]] ([[User talk:BrianZ|talk]]) 00:52, 20 April 2020 (UTC)

== Math and Error bars ==

Well this is surprising came here thinking I understood it just to see what the discussion looked like. Ended up learning something new. I was able to understand intuitively the comic. But this is my first exposure to actually doing math on the error bars. I think I was supposed to do that in college but I don't remember anyone ever explaining how it should work. --[[Special:Contributions/162.158.63.208|162.158.63.208]] 18:14, 17 April 2020 (UTC)

In recent days, there have been a number of math "quizzes" in this same type of format, albeit generally with only addition and maybe multiplication, appearing on Facebook. Should the explanation include a reference to this as a possible contributing reason for Randall's comic? One could also argue that those quizzes have been appearing on Facebook as a way to spend/waste time during the coronavirus pandemic lock-down, making he comic at least tangentially related to Covid19 LIES.
:: Unsigned vandalism? /\ [https://www.explainxkcd.com/wiki/index.php?title=Talk:2295:_Garbage_Math&diff=190866&oldid=190856 change history] @user Please feel free to move your discussion to an appropriate forum and remove both the edit and this comment at such time. [[User:Iggynelix|Iggynelix]] ([[User talk:Iggynelix|talk]])

What's the difference between relative error and absolute error? I don't understand these terms. Maybe add?
: Absolute error is the amount of uncertainty in a value measured as a given number. e.g. 5.7 ± 1.2 means that actual value lies somewhere between 5.7 - 1.2 and 5.7 + 1.2 = 4.5 to 6.9. If you change the 5.7 to another value, you still get the same absolute difference of maximum and minimum values. Relative error depends on the value you are comparing to. e.g. 5.7 ± 10% would be between 5.7 - 0.57 and 5.7 + 0.57 = 5.13 to 6.27. The absolute difference of maximum and minimum would change if the main number changes. e.g. 11.3 ± 10% would be between 10.17 and 12.43, which has a greater absolute difference of maximum and minimum than the previous example. [[User:Nutster|Nutster]] ([[User talk:Nutster|talk]]) 01:54, 18 April 2020 (UTC)

Are all of these equations consistent with garbage = infinity?
: Unfortunately, as written, these equations would not make sense by defining Garbage as an infinity. Infinity is not a number you can count to or measure in between integers. Infinity is the idea of unending-ness. Trying to use infinity as if it a finite number yields all sorts of invalid results. In this case Garbage is defined as an arbitrary finite number with a large amount of uncertainty in its value. [[User:Nutster|Nutster]] ([[User talk:Nutster|talk]]) 01:40, 18 April 2020 (UTC)
::: That's a pretty good definition of 'garbage' in ''any'' case, plus or minus 10%. ( See also [https://www.weforum.org/agenda/2017/06/landfill-mining-recycling-eurelco/ valuable garbage]) [[User:Iggynelix|Iggynelix]] ([[User talk:Iggynelix|talk]]) 14:19, 18 April 2020 (UTC)

Would the summation divided by ''n'' just give you the arithmatic mean of the data set? [[User:Nutster|Nutster]] ([[User talk:Nutster|talk]]) 01:55, 18 April 2020 (UTC)
:Pretty much, but the point is probably more that (without consistent bias across the set, just 'random' errors for each item) it suppresses the degree of garbagicity as outliers are increasingly nullified by the greater number of more competently accurate values and (if it's a symmetric error) opposing outliers. [[Special:Contributions/162.158.34.222|162.158.34.222]] 09:29, 18 April 2020 (UTC)

The statement that NaN^0 isn't fully justified and I'm not clear it belongs. [[User:Djbrasier|Djbrasier]] ([[User talk:Djbrasier|talk]]) 18:46, 18 April 2020 (UTC)
: I agree... It also isn't evident to me that this comic has anything to do with floating-point math, which is the only thing that could (even slimly) justify its inclusion. This is about statistics, not programming. --[[Special:Contributions/108.162.215.12|108.162.215.12]] 05:25, 19 April 2020 (UTC)

I'm concerned that, with "Precise Number" there's the usual confusion between Accuracy and Precision (''edit: and of course Resolution, too!''). A precise number can still be utter garbage, as 84.7489327(646475)% of all mathematicians could tell you. [[Special:Contributions/162.158.111.241|162.158.111.241]] 13:59, 19 April 2020 (UTC)
:The table of formulae for the propagation of variance σ addresses that aspect. You can't know the accuracy of a result without knowing the precision of its calculation, and while reducing precision always reduces accuracy, it's not the other way around. But precision is inherent in the representation and operations, while accuracy is secondary when you aren't discussing the initial measurements of the inputs, so I think the terminology is correct.
:By the way, shout out to [https://www.explainxkcd.com/wiki/index.php?title=2295%3A_Garbage_Math&type=revision&diff=190882&oldid=190870 172.68.51.124] for filling out all but one of those table entries between the two of them. I wonder where they looked them up. I'm guessing a ''CRC Handbook'' left over from High School chemistry or some such? Anyway, good job! This really looks classy now that it's been cleaned up a bit. [[Special:Contributions/162.158.255.64|162.158.255.64]] 06:45, 20 April 2020 (UTC)

Talk:2295: Garbage Math

2020-04-20T06:45:41Z

162.158.255.64: /* Math and Error bars */ reply

== Inclusion in Series ==
This is not a Covid19 comic. One could think that this is a comment on the difficulties of modeling the corona virus outbreak, but since discussions of exponential functions are only a small part in the comic I believe it is just a general comment on floating point arithmetic mixed in with statistical considerations. --[[Special:Contributions/108.162.229.242|108.162.229.242]] 17:28, 17 April 2020 (UTC)
:I disagree that this is not a COVID-19 comic. I also believe the one about visualizing large numbers was COVID-19 related. On the other hand, I like the idea that Randall might produce exactly 19 comics related to SARS CoViD 2019, so I'm prepared to concede the point for the sake of arbitrary numerological appeal.
:[[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 18:42, 17 April 2020 (UTC)
::I think Exa-Exabyte was a real stretch (the virus doesn't even have DNA), but there is a tenuous link so whatever. The idea that ''this'' comic is related, on the other hand, stretches past the breaking point. There's hardly anything that can't be linked to global events if we try hard enough, but that doesn't mean there's an actual link. Sometimes a comic about garbage math is just a comic about garbage math. [[Special:Contributions/172.69.71.58|172.69.71.58]] 19:33, 17 April 2020 (UTC)
:::I think this one's much more likely to be a coronavirus comic than Exa-Exabyte was. There's an awful lot of COVID data, much of it either very imprecise or outright garbage; and the comic directly before this one ([[2294]]) involved bad modeling of said COVID data, so clearly COVID data (and its limitations) is something Randall's currently thinking of and drawing comics about. [[User:Pelosujamo|Pelosujamo]] ([[User talk:Pelosujamo|talk]]) 20:25, 17 April 2020 (UTC)
::::Exa-Exabyte was centered around biology, which gives reason to believe it was covid19 related. This one seems much more uncertain. Any conclusion that it is related is based on garbage. Jokes aside, It seems like much more of a stretch to me. Randall thinking in those terms is a reasonable argument, but personally I am going to assume this is the chain breaker unless a direct reference is made in the next couple comics since ending at 19 is would be appropriate. [[Special:Contributions/172.69.70.209|172.69.70.209]]
:: While this comic has no ''direct'' reference to Covid-19 it does appear that the math might be related. At this point we can't know if the series has ended. As such I've edited the paragraph in the explanation to identify the known ambiguities. And now I realize I've made an explanatory paragraph about "knowledge error bars" in the explanation of a comic about numerical error bars.[[User:Iggynelix|Iggynelix]] ([[User talk:Iggynelix|talk]]) 14:42, 18 April 2020 (UTC)
:::No. The reason it appears the math might be related is ''because the math relates to everything, everywhere''. That's not enough of a connection. During this pandemic, there will be a lot of comics related to the coronavirus, many of them in a row, but that doesn't mean that every comic that could be tangentially related if you squint just right should qualify as a COVID-19 comic (I ''still'' think Exa-Exabyte doesn't). There needs to be a real link, because just about ''anything'' could be twisted into a relation if you try hard enough. As a test, I hit [[Special:Random]] and got [[346: Diet Coke+Mentos]]. Wouldn't you know, that's a coronavirus comic! The father, you see, actually had COVID-19 and died, but Diet Coke and Mentos has brought him back! No. The line should be drawn here. The streak has ended. [[Special:Contributions/172.69.68.197|172.69.68.197]] 17:02, 18 April 2020 (UTC)
::::I agree this is not a serious contender for inclusion as a COVID comic. Although I'm pretty sure Randall has input to COVID19 models as garbage on his mind. But there is nothing in this comic that suggest this math be used on a pandemic. The exa byte is a different story as it is about how much of biology we cannot know or control in the midst of a lot of comics about some new biology we do not control. I do not expect that this will end the covid19 series, but I will consent that even if the next comic is a clear corona comic, it will no longer be an unbroken streak. Anyway the real streak ended at the end of March with the late April Fool's comic. I also do not at all think that the coke mentos could be seen as a COVID19 comic, that is just bulls**t trying to prove a point that I believe you fail completely. I also tried random comic (I like the idea) and found [[1208: Footnote Labyrinths]]. It is a scientific paper (with nested footnotes) and given science, we could say it was about science about Corona. Naah. But for the same reason this comic should not be considered corona. --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 20:53, 18 April 2020 (UTC)

:::::I am pretty sure this IS related. Right now, everybody and his grandmother is staring at the Johns Hopkins Coronavirus numbers for different countries. Entire newspaper articles are written about these numbers and about why one country is apparently faring better than the other and what this means. The numbers are made into fancy graphics. People use these numbers to calculate fatality rates and cure rates. Politicians might even use these numbers to make decisions.
:::::And all this even though everybody KNOWS that the numbers cannot really be compared from one country to the other, because testing prerequisites vary, testing availability varies, testing procedures vary, criteria used to include a death as a coronavirus death vary. The sources of the numbers are very different and might not always be reliable. [Apparently, they include local language newspapers, website and even social media accounts. How many people DOES the Johns Hopkins University have to track all these sources reliably, worldwide, in local languages?] And not to forget some countries probably are downright lying.
:::::And still, people are comparing. I've read articles where the author admits the numbers are probably garbage in one sentence and then STILL goes on to calculate fatality rates from them in the next sentence. So, most PROBABLY related.

::::::I challenge you to find a comic in the archive that can't be twisted to say it's related to COVID-19. At this point people are finding connections in the same way that people analyze "the curtain is blue". [[Special:Contributions/108.162.245.26|108.162.245.26]] 22:06, 19 April 2020 (UTC)
--[[Special:Contributions/141.101.69.153|141.101.69.153]] 21:53, 19 April 2020 (UTC)

This comic very much reminds me of this article: [https://www.realclearmarkets.com/articles/2020/04/17/its_decidedly_not_the_math_its_always_people_489344.html
It's Decidedly Not the Math. It's Always People] So much so that my first thought was that the comic was inspired by it, though of course I can't prove it.[[User:BrianZ|BrianZ]] ([[User talk:BrianZ|talk]]) 00:52, 20 April 2020 (UTC)

== Math and Error bars ==

Well this is surprising came here thinking I understood it just to see what the discussion looked like. Ended up learning something new. I was able to understand intuitively the comic. But this is my first exposure to actually doing math on the error bars. I think I was supposed to do that in college but I don't remember anyone ever explaining how it should work. --[[Special:Contributions/162.158.63.208|162.158.63.208]] 18:14, 17 April 2020 (UTC)

In recent days, there have been a number of math "quizzes" in this same type of format, albeit generally with only addition and maybe multiplication, appearing on Facebook. Should the explanation include a reference to this as a possible contributing reason for Randall's comic? One could also argue that those quizzes have been appearing on Facebook as a way to spend/waste time during the coronavirus pandemic lock-down, making he comic at least tangentially related to Covid19 LIES.
:: Unsigned vandalism? /\ [https://www.explainxkcd.com/wiki/index.php?title=Talk:2295:_Garbage_Math&diff=190866&oldid=190856 change history] @user Please feel free to move your discussion to an appropriate forum and remove both the edit and this comment at such time. [[User:Iggynelix|Iggynelix]] ([[User talk:Iggynelix|talk]])

What's the difference between relative error and absolute error? I don't understand these terms. Maybe add?
: Absolute error is the amount of uncertainty in a value measured as a given number. e.g. 5.7 ± 1.2 means that actual value lies somewhere between 5.7 - 1.2 and 5.7 + 1.2 = 4.5 to 6.9. If you change the 5.7 to another value, you still get the same absolute difference of maximum and minimum values. Relative error depends on the value you are comparing to. e.g. 5.7 ± 10% would be between 5.7 - 0.57 and 5.7 + 0.57 = 5.13 to 6.27. The absolute difference of maximum and minimum would change if the main number changes. e.g. 11.3 ± 10% would be between 10.17 and 12.43, which has a greater absolute difference of maximum and minimum than the previous example. [[User:Nutster|Nutster]] ([[User talk:Nutster|talk]]) 01:54, 18 April 2020 (UTC)

Are all of these equations consistent with garbage = infinity?
: Unfortunately, as written, these equations would not make sense by defining Garbage as an infinity. Infinity is not a number you can count to or measure in between integers. Infinity is the idea of unending-ness. Trying to use infinity as if it a finite number yields all sorts of invalid results. In this case Garbage is defined as an arbitrary finite number with a large amount of uncertainty in its value. [[User:Nutster|Nutster]] ([[User talk:Nutster|talk]]) 01:40, 18 April 2020 (UTC)
::: That's a pretty good definition of 'garbage' in ''any'' case, plus or minus 10%. ( See also [https://www.weforum.org/agenda/2017/06/landfill-mining-recycling-eurelco/ valuable garbage]) [[User:Iggynelix|Iggynelix]] ([[User talk:Iggynelix|talk]]) 14:19, 18 April 2020 (UTC)

Would the summation divided by ''n'' just give you the arithmatic mean of the data set? [[User:Nutster|Nutster]] ([[User talk:Nutster|talk]]) 01:55, 18 April 2020 (UTC)
:Pretty much, but the point is probably more that (without consistent bias across the set, just 'random' errors for each item) it suppresses the degree of garbagicity as outliers are increasingly nullified by the greater number of more competently accurate values and (if it's a symmetric error) opposing outliers. [[Special:Contributions/162.158.34.222|162.158.34.222]] 09:29, 18 April 2020 (UTC)

The statement that NaN^0 isn't fully justified and I'm not clear it belongs. [[User:Djbrasier|Djbrasier]] ([[User talk:Djbrasier|talk]]) 18:46, 18 April 2020 (UTC)
: I agree... It also isn't evident to me that this comic has anything to do with floating-point math, which is the only thing that could (even slimly) justify its inclusion. This is about statistics, not programming. --[[Special:Contributions/108.162.215.12|108.162.215.12]] 05:25, 19 April 2020 (UTC)

I'm concerned that, with "Precise Number" there's the usual confusion between Accuracy and Precision (''edit: and of course Resolution, too!''). A precise number can still be utter garbage, as 84.7489327(646475)% of all mathematicians could tell you. [[Special:Contributions/162.158.111.241|162.158.111.241]] 13:59, 19 April 2020 (UTC)
:The table of formulae for the propagation of σ addresses that aspect. You can't know the accuracy of a result without knowing the precision of its calculation, and while reducing precision always reduces accuracy, it's not the other way around. But precision is inherent in the representation and operations, while accuracy is secondary when you aren't discussing the initial measurements of the inputs, so I think the terminology is correct.
:By the way, shout out to [https://www.explainxkcd.com/wiki/index.php?title=2295%3A_Garbage_Math&type=revision&diff=190882&oldid=190870 172.68.51.124] and [https://www.explainxkcd.com/wiki/index.php?title=2295:_Garbage_Math&diff=prev&oldid=190882 172.68.51.124] for filling out all but one of those table entries between the two of them. I wonder where they looked them up. I'm guessing a ''CRC Handbook'' left over from High School chemistry or some such? Anyway, good job editors, this really looks classy now that it's been cleaned up a bit. [[Special:Contributions/162.158.255.64|162.158.255.64]] 06:45, 20 April 2020 (UTC)

438: Internet Argument

2020-03-08T22:07:23Z

162.158.255.64: They're probably not trolls.

{{comic
| number = 438
| date = June 18, 2008
| title = Internet Argument
| image = internet argument.png
| titletext = It's easier to be an asshole to words than to people.
}}

==Explanation==
Since the first time the internet made possible to have sustained conversations with people in remote locations, it was found that most people tend to use harsh language in these conversations much more often than they would with regular spoken face-to-face conversations. This effect is similar to what happens when people drive a car: they're much more likely to get exasperated or angry at other drivers than they would when not driving.

In the first two panels, [[Cueball]] is having some harsh words and probably insults with the other [[Cueball]]. [[Megan]] takes hold of Cueball and flies him to the other one, so they see each other face to face. In this situation, they both remain silent as none of them find anything to say to the other.

When Megan returns Cueball to his original computer, both keep their conversation, but without the insults.

The title text just summarizes the whole idea into a single sentence.

==Transcript==
:[Cueball is typing profanities into his computer.]
:[Friend is typing profanities into his computer.]
:[Megan floats in behind Cueball.]
:[Megan lifts Cueball.]
:[They are flying over mountains.]
:[Megan and Cueball are floating in front of the friend and his computer.]
:[She sets Cueball down in front of the friend and his computer.]
:[Megan lifts Cueball again.]
:[They are flying.]
:[Megan sets Cueball down in his chair at his computer.]
:[Cueball is typing at his computer.]
:[Friend is typing at his computer.]

{{comic discussion}}
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Megan]]
[[Category:Internet]]
[[Category:Multiple Cueballs]]

Talk:440: Road Rage

2018-01-07T06:53:11Z

162.158.255.64:

;Incomplete (as of August 26, 2013)
*At the title text Black Hat is avoiding a crash.
*While many explains are monster explains, here is the WIFI missing, this explain is just more a transcript.--[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 21:44, 26 August 2013 (UTC)
The idea is that the tailgater (I'll name him Phil for ease of understanding) will be distracted while he contemplates his loss, so when Black Hat slams on the brakes, Phil hopefully won't have enough stopping distance to avoid a collision, slamming into Black Hat's car. The accident is always caused by the car behind, meaning Phil will be at fault.[[User:Lyusternik|Lyusternik]] ([[User talk:Lyusternik|talk]]) 15:26, 2 December 2013 (UTC)

Okay, I've been bold, completely rewrote the explanation AND removed the incomplete banner. It now looks less like a transcript and (I think) everything is covered. [[Special:Contributions/173.245.53.161|173.245.53.161]] 17:28, 19 February 2014 (UTC)

Whew, I've been more offensive than Black Hat in the past and I'm still happy today that I did survive this. I did not slam the brake, no stoplight, just releasing my foot from the gas pedal at high speed and my car slowed down without any warning to the one behind me. There was happily no accident and NEVER TRY SOMETHING LIKE THIS. But after this incident the guy did slam his own brake and he never did try to overtake me again. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 21:36, 2 June 2014 (UTC)

In light of the last paragraph of the explanation, I wish Randall's drawing made it clear whether BH and Danish were wearing seatbelts. [[Special:Contributions/173.245.54.52|173.245.54.52]] 19:45, 30 October 2015 (UTC)

I think that Danish does not survive the accident that she provoked with her message to the tailgating guy. This is a very nice example of a self-fulfilling prophecy.--[[Special:Contributions/141.101.75.18|141.101.75.18]] 14:28, 25 January 2016 (UTC)

No one tried to guess at why the shot in the dark worked? I thought it might have something to do with the fact that tailgaters tend to be reckless drivers and he had caused someone to die before due to his reckless driving. [[User:Flewk|flewk]] ([[User talk:Flewk|talk]]) 17:56, 28 December 2015 (UTC)

Revisiting this comic after watching 13 Reasons Why really gives you a new view on the whole thing. I wonder if the book, or indeed any specific work, was involved in Randall's creative process for this comic, or if he just pulled the idea for the guilt trip out of thin air. [[Special:Contributions/162.158.255.64|162.158.255.64]] 06:53, 7 January 2018 (UTC)

1850: Air Force Museum

2017-06-14T19:02:23Z

162.158.255.64: /* Explanation */ wording

{{comic
| number = 1850
| date = June 14, 2017
| title = Air Force Museum
| image = air_force_museum.png
| titletext = I had fun visiting the museum at Dover Air Force Base, unless they don't have a museum, in which case I've never been to Delaware in my life.
}}

==Explanation==
{{incomplete| Perhaps more detail is needed?}}
[[Megan]] asks [[Cueball]] about his day. He tells about his visit to a military {{w|Aviation museum|aircraft museum}} at the {{w|Military air base|air force base}} and lists some of the things he saw. It starts with things you would expect at a typical museum, such as a mix of modern, older, and even older aircraft, before revealing the fact that Cueball was able to watch missiles being loaded, which is something that would be extremely out of place and dangerous at a museum. Realizing this, Cueball remarks that he hopes that he was at a museum, and Megan asks him if he hears helicopters. The implication is that there was no museum to begin with and Cueball went to observe the actual air force base and is now being pursued by the military.

The mention of "planes from different eras" alludes to the fact that military aircraft are often still in use after a much longer time than they were originally designed for. Examples of this are the US Air Force's B-52 bomber, first introduced in 1955 (62 years before the publication of this comic) and the C-160 Transall, which has been in service in, e.g., the German Luftwaffe, since 1967 (50 years before). Additionally, aircraft museums typically house military aircraft from previous eras, such as from WWII and the Cold War, to show the evolution in aircraft design and to showcase technological advances.

The title text builds on this premise. Cueball says that he had fun visiting another Air Force "museum", but he adds that if they don't have a museum (in which case he was trespassing on a military base) then he denies going anywhere near it. Fortunately for Cueball, there is in fact an Air Force museum nearby: the {{w|Air Mobility Command Museum}} about half a mile south of the {{w|Dover Air Force Base}}.

==Transcript==
:[Megan walks from left over to Cueball.]
:Megan: How was your day?
:Cueball: I visited the military aircraft museum over at the Air Force base. It was really neat!

:[Both walking together to the right.]
:Cueball: They have planes from different eras, all kinds of cool equipment, and you can even watch missiles being loaded.

:[Both walking while they contemplate.]

:[Both still walking.]
:Cueball: ...at least, I ''hope'' that was a museum.
:Megan: Do you hear helicopters?

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Megan]]

1850: Air Force Museum

2017-06-14T19:01:50Z

162.158.255.64: alternative explanation

{{comic
| number = 1850
| date = June 14, 2017
| title = Air Force Museum
| image = air_force_museum.png
| titletext = I had fun visiting the museum at Dover Air Force Base, unless they don't have a museum, in which case I've never been to Delaware in my life.
}}

==Explanation==
{{incomplete| Perhaps more detail is needed?}}
[[Megan]] asks [[Cueball]] about his day. He tells about his visit to a military {{w|Aviation museum|aircraft museum}} at the {{w|Military air base|air force base}} and lists some of the things he saw. It starts with things you would expect at a typical museum, such as a mix of modern, older, and even older aircraft, before revealing the fact that Cueball was able to watch missiles being loaded, which is something that would be extremely out of place and dangerous at a museum. Realizing this, Cueball remarks that he hopes that he was at a museum, and Megan asks him if he hears helicopters. The implication is that there was no museum to begin with and Cueball went to observe the actual air force base and is now being pursued by the military.

The mention of "planes from different eras" alludes to the fact that military aircraft are often still in use after a much longer time than they were originally designed for. Examples of this are the US Air Force's B-52 bomber, first introduced in 1955 (62 years before the publication of this comic) and the C-160 Transall, which has been in service in, e.g., the German Luftwaffe, since 1967 (50 years before). Alternatively, aircraft museums typically house military aircraft from previous eras, such as from WWII and the Cold War, to show the evolution in aircraft design and to showcase technological advances.

The title text builds on this premise. Cueball says that he had fun visiting another Air Force "museum", but he adds that if they don't have a museum (in which case he was trespassing on a military base) then he denies going anywhere near it. Fortunately for Cueball, there is in fact an Air Force museum nearby: the {{w|Air Mobility Command Museum}} about half a mile south of the {{w|Dover Air Force Base}}.

==Transcript==
:[Megan walks from left over to Cueball.]
:Megan: How was your day?
:Cueball: I visited the military aircraft museum over at the Air Force base. It was really neat!

:[Both walking together to the right.]
:Cueball: They have planes from different eras, all kinds of cool equipment, and you can even watch missiles being loaded.

:[Both walking while they contemplate.]

:[Both still walking.]
:Cueball: ...at least, I ''hope'' that was a museum.
:Megan: Do you hear helicopters?

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Megan]]

1849: Decades

2017-06-13T00:26:02Z

162.158.255.64: /* Explanation */ already mentioned above

{{comic
| number = 1849
| date = June 12, 2017
| title = Decades
| image = decades.png
| titletext = In the 90s, our variety radio station used the tagline "the best music of the 70s, 80s, and 90s." After 2000, they switched to "the best music of the 80s, 90s, and today." I figured they'd change again in 2010, but it's 2017 and they're still saying "80s, 90s, and today." I hope radio survives long enough for us to find out how they deal with the 2020s.
}}

==Explanation==
{{incomplete|Title text not explained.}}

This comic shows, by use on a time-line, an interesting phenomenon where music, fashion, movies and culture created between the years 2000 and 2020 are not commonly grouped into the decade in which they were produced like previous decades. The comic asserts the reason for this is the lack of a single clear term to describe these decades, stating that the term "{{w|2000s}}" is ambiguous (as it could refer to the decade, century or millennium as a whole) and the terms "Aughts" and "Teens" never became the widely accepted terms for these decades.

The time-line in the comic stretches into the future (as of the time of publication) and attempts to name the 2020-2029 decade as the 20s, but does so with an uncertain question mark, presumably because it's (presently) an open question whether this dating convention will be reinstated after a 20-year pause. As the comic points out, common vernacular has managed to operate without clear terms for that grouping for 17 years, and that may have left enough of a mark on our thinking that we'll simply continue to operate in that way. There's an argument to be made grouping culture by decades is fairly arbitrary and not essential in cultural discussions. It should also be considered that that "the twenties" is still occasionally used to refer to the 1920's, and so reusing it to refer to the 2020's could be a source of confusion. It's not impossible that decade-based grouping will fall out of favor all together in the 21st century.

The title text talks about Randall's local radio station. In the 90s, they were able to use clear decade groupings. Once the year 2000 hit, they began saying "today", avoiding aughts or 2000s, which, as Randall says, never gained popular support. When 2010 hit, Randall believed they would switch their format, having left the awkwardness of the 00s. However, they kept their format to this day, finishing using teens or 10s to be confusing as well. Randall expresses interest in what change they will include in the 2020s (changing to the 20s or continuing their format), should radio last that long.

==Error==

Randall writes, presumably by mistake, "and and aughts" in the caption for this comic, instead of "and aughts". This changes the caption from his presumptive goal of "It's weird how for 20 years we stopped grouping our cultural memories by decade because "2000s" is ambiguous and "Aughts" and "Teens" never really stuck." to "It's weird how for 20 years we stopped grouping our cultural memories by decade because "2000s" is ambiguous and and "Aughts" and "Teens" never really stuck."

==Transcript==
:[A time line across the top of the box marks decades from 1960 to 2030, the labels are above the line and the ticks marking each decade are below.]

:[Label: 1960]
:60s Music; 60s Fashion; 60s Movies; 60s Culture

:[Label: 1970]
:70s Music; 70s Fashion; 70s Movies; 70s Culture

:[Label: 1980]
:80s Music; 80s Fashion; 80s Movies; 80s Culture

:[Label: 1990]
:90s Music; 90s Fashion; 90s Movies; 90s Culture

:[Label: 2000 and 2010]
:[Items grouped over two decades.]
:Fashion; Culture; Music; Movies

:[Label: 2020]
:[The text is in light grey font.]
:20s Music?; 20s Fashion?; 20s Movies?; 20s Culture?

:[Label: 2030]

:[Caption below the panel:]
:It's weird how for 20 years we stopped grouping our cultural memories by decade because "2000s" is ambiguous and and "Aughts" and "Teens" never really stuck.

{{comic discussion}}

1833: Code Quality 3

2017-05-05T20:07:25Z

162.158.255.64: /* Explanation */ fix

{{comic
| number = 1833
| date = May 5, 2017
| title = Code Quality 3
| image = code_quality_3.png
| titletext = It's like a half-solved cryptogram where the solution is a piece of FORTH code written by someone who doesn't know FORTH.
}}

==Explanation==
{{incomplete|Still needs to explain what example code is.}}

This comic is a direct continuation of [[1513: Code Quality]] and [[1695: Code Quality 2]] in the [[:Category:Code Quality|Code Quality]] series, in which Ponytail continually insults Cueball's code style. In this comic, as in the previous, Cueball does not directly appear, only speaking off-panel; however, as it is a continuation of the series, it is clear that this is Cueball's code.

In the first panel, Ponytail references {{w|query string|query strings}}, which store information, such as search queries or page numbers, relevant to the URL. Query strings are not meant to be especially human-readable, so a song based on one would likely not be a good one{{Citation needed}}.

A tactical flashlight is a light that can be mounted on a gun for use in low-light scenarios. They tend to be very durable and very bright. Different models have different features and capabilities, so they are given cool-sounding model numbers. A JSON table of these model numbers would look like random data.

{{w|Alan Turing}} was a British theoretical computer scientist, often considered the father of the field. His 1936 paper outlined Turing machines, a theoretical model for computing, as well as computability and the halting problem. Theoretical computer science is very different from practical coding; understanding the contents of the paper would not at all help a coder to understand today's algorithms, design patterns, and best practices. This is only slightly helped by a page of Javascript example code. Javascript is a popular programming language, and example code is used to explain a concept in programming or demonstrate how a program works. Because it will only help with this one concept or program, it is impossible to learn everything necessary to make high-quality programs with just one piece of example code.

In the final panel, Ponytail references {{w|leet|leet-speak}}, in which symbols are replaced with similar-looking symbols, and a {{w|manifesto}}, a statement of a person or group's beliefs and intentions. A manifesto from a survivalist cult leader might be nonsensical, even before being translated to leet-speak. Memory allocation is a low-level computer programming concept; most modern languages have features that take care of memory allocation for the programmer, possibly implying that Cueball does not know how to use these features.

At this point Cueball, quickly becoming impatient with Ponytail's sass, retorts that if she can't start giving him the constructive criticism that he's looking for, he can always find someone else to replace her. Ponytail smugly responds that nobody else would be able to stomach his code for more than one sitting, and that she's the only one he's got.

{{w|Forth_(programming_language)#Programmer.27s_perspective|Forth}} is an old programming language that tends to be difficult to read. A {{w|cryptogram}} is a cipher puzzle, generally one easy enough to be solved manually. The title text implies that the code is so bad that it looks like unreadable FORTH code that is missing random characters.

==Transcript==
:[Ponytail sitting in front of a computer screen typing. Cueball speaks only off-panel, but since this is a direct continuation of comic 1513 and 1695: Code Quality and Code Quality 2 where Cueball is shown, there can be no doubt it is him.]
:Ponytail: Your code looks like song lyrics written using only the stuff that comes after the question mark in a URL.
:Cueball (off-panel): Sorry.
:[Zoom in on Ponytail's upper body.]
:Ponytail: It's like a JSON table of model numbers for flashlights with "tactical" in their names.
:[Zoom back out again. Ponytail has lifted her hands off the table.]
:Ponytail: Like you read Turing's 1936 paper on computing and a page of JavaScript example code and guessed at everything in between.
:[Zoom in again on Ponytail's face.]
:Ponytail: It's like a leet-speak translation of a manifesto by a survivalist cult leader who's for some reason obsessed with memory allocation.
:Cueball (off-panel): I can get someone else to review my code.
:Ponytail: Not more than once, I bet.

{{comic discussion}}

[[Category:Code Quality]]

1826: Birdwatching

2017-04-19T16:30:55Z

162.158.255.64: /* Explanation */ is he using a camera?

{{comic
| number = 1826
| date = April 19, 2017
| title = Birdwatching
| image = birdwatching_small.png
| titletext = No, tell the park rangers to calm down, it's fine--I put a screen on the front. I just want to get the birds a little closer.
}}

==Explanation==
{{incomplete|Needs more information on birdwatching.}}

{{w|Birdwatching}} is an activity to observe birds. Usually this is done at a distance, as birds are flying in the air, and are far away. Cueball notes that even with {{w|binoculars}} (or a camera?), the birds are different to see because of their distance.

Cueball's solution is to use a {{w|vacuum cleaner}}, specifically a {{w|shop vac}}, to pull in the birds. This is physically impossible with such a small device. Even if the shop vac created a perfect vacuum, it can only pull out air at the speed of sound, which amounts to approximately 1 cubic meter per second considering the apparent size of the hose. This is not enough to create a significant amount of wind or affect the atmosphere.

The title text refers to {{w|park ranger}}s, who would naturally be distressed by birds being forced to coalesce via an extremely powerful vacuum. If such a vacuum were created and used for this purpose, it probably would pose a threat to said birds. Cueball says he has solved this problem by placing a perforated screen in front. In doing so, he can safely attract the birds without trapping them inside the vacuum. He implies that this should remove the danger to the birds, which is not the case. While the birds can no longer enter the vacuum itself, having a large number of birds pulled into a (presumably small) screen would probably fare poorly for the birds, so Cueball's solution is rather poor.

==Trivia==
This comic was was originally published with a large picture size, much larger than the standard screen, due to its link pointing to [https://imgs.xkcd.com/comics/birdwatching_huge.png birdwatching_huge.png]. It was later updated to point to an image at the usual size.

==Transcript==
:[Cueball and Beanie Man are standing with camera and binoculars.]
:Cueball: Birdwatching is hard. They're all too small and far away.

:[Both raise tool eyepiece.]
:Cueball: That Hawk is over a mile up! How did you even spot it?

:[Both, lower eyepiece. Cueball looks down, fuming.]

:[Cueball now has a SHOP VAC and has it pointed to the sky.]
:Shop Vac: WHRRRRRR
:[Beanie Guy looks at Cueball, confused.]

{{comic discussion}}

1826: Birdwatching

2017-04-19T16:30:12Z

162.158.255.64: add back incomplete template - should wait for more updates

{{comic
| number = 1826
| date = April 19, 2017
| title = Birdwatching
| image = birdwatching_small.png
| titletext = No, tell the park rangers to calm down, it's fine--I put a screen on the front. I just want to get the birds a little closer.
}}

==Explanation==
{{incomplete|Needs more information on birdwatching.}}

{{w|Birdwatching}} is an activity to observe birds. Usually this is done at a distance, as birds are flying in the air, and are far away. Cueball notes that even with {{w|binoculars}}, the birds are different to see because of their distance.

Cueball's solution is to use a {{w|vacuum cleaner}}, specifically a {{w|shop vac}}, to pull in the birds. This is physically impossible with such a small device. Even if the shop vac created a perfect vacuum, it can only pull out air at the speed of sound, which amounts to approximately 1 cubic meter per second considering the apparent size of the hose. This is not enough to create a significant amount of wind or affect the atmosphere.

The title text refers to {{w|park ranger}}s, who would naturally be distressed by birds being forced to coalesce via an extremely powerful vacuum. If such a vacuum were created and used for this purpose, it probably would pose a threat to said birds. Cueball says he has solved this problem by placing a perforated screen in front. In doing so, he can safely attract the birds without trapping them inside the vacuum. He implies that this should remove the danger to the birds, which is not the case. While the birds can no longer enter the vacuum itself, having a large number of birds pulled into a (presumably small) screen would probably fare poorly for the birds, so Cueball's solution is rather poor.

==Trivia==
This comic was was originally published with a large picture size, much larger than the standard screen, due to its link pointing to [https://imgs.xkcd.com/comics/birdwatching_huge.png birdwatching_huge.png]. It was later updated to point to an image at the usual size.

==Transcript==
:[Cueball and Beanie Man are standing with camera and binoculars.]
:Cueball: Birdwatching is hard. They're all too small and far away.

:[Both raise tool eyepiece.]
:Cueball: That Hawk is over a mile up! How did you even spot it?

:[Both, lower eyepiece. Cueball looks down, fuming.]

:[Cueball now has a SHOP VAC and has it pointed to the sky.]
:Shop Vac: WHRRRRRR
:[Beanie Guy looks at Cueball, confused.]

{{comic discussion}}

1826: Birdwatching

2017-04-19T16:28:43Z

162.158.255.64: brief explanation of birdwatching

{{comic
| number = 1826
| date = April 19, 2017
| title = Birdwatching
| image = birdwatching_small.png
| titletext = No, tell the park rangers to calm down, it's fine--I put a screen on the front. I just want to get the birds a little closer.
}}

==Explanation==
{{w|Birdwatching}} is an activity to observe birds. Usually this is done at a distance, as birds are flying in the air, and are far away. Cueball notes that even with {{w|binoculars}}, the birds are different to see because of their distance.

Cueball's solution is to use a {{w|vacuum cleaner}}, specifically a {{w|shop vac}}, to pull in the birds. This is physically impossible with such a small device. Even if the shop vac created a perfect vacuum, it can only pull out air at the speed of sound, which amounts to approximately 1 cubic meter per second considering the apparent size of the hose. This is not enough to create a significant amount of wind or affect the atmosphere.

The title text refers to {{w|park ranger}}s, who would naturally be distressed by birds being forced to coalesce via an extremely powerful vacuum. If such a vacuum were created and used for this purpose, it probably would pose a threat to said birds. Cueball says he has solved this problem by placing a perforated screen in front. In doing so, he can safely attract the birds without trapping them inside the vacuum. He implies that this should remove the danger to the birds, which is not the case. While the birds can no longer enter the vacuum itself, having a large number of birds pulled into a (presumably small) screen would probably fare poorly for the birds, so Cueball's solution is rather poor.

==Trivia==
This comic was was originally published with a large picture size, much larger than the standard screen, due to its link pointing to [https://imgs.xkcd.com/comics/birdwatching_huge.png birdwatching_huge.png]. It was later updated to point to an image at the usual size.

==Transcript==
:[Cueball and Beanie Man are standing with camera and binoculars.]
:Cueball: Birdwatching is hard. They're all too small and far away.

:[Both raise tool eyepiece.]
:Cueball: That Hawk is over a mile up! How did you even spot it?

:[Both, lower eyepiece. Cueball looks down, fuming.]

:[Cueball now has a SHOP VAC and has it pointed to the sky.]
:Shop Vac: WHRRRRRR
:[Beanie Guy looks at Cueball, confused.]

{{comic discussion}}

415: Restraining Order

2017-02-07T22:30:43Z

162.158.255.64: /* Explanation */

{{comic
| number =415
| date =April 25, 2008
| title =Restraining Order
| image =restraining_order.png
| titletext =On Mondays I go running, so you'll have to get up early and follow along a parallel street. What fun!
}}

==Explanation==
A {{w|restraining order}} is a legal injunction requiring a party to do, or refrain from doing, certain acts, under penalty of fines or imprisonment, designed to safeguard the complainant's life. In general the forbidden act is virtually always contacting the complainant in any way, and enforcing they remain a minimum distance from the complainant is given far less gravitas and emphasis than media usually portrays. Even when a minimum distance is made a critical aspect, a ''maximum'' distance is never set.

The joke in this comic is that [[Ponytail]] has gotten a restraining order against [[Cueball]] that requires him to stay between 500 yards (~457 m) and 600 yards (~549 m) of her at ''all times,'' which needless to say, will cause a major disruption to his life.

The title text says he'll have to get up early on Mondays and follow her jogging course along a parallel street.

A {{w|yard}} is a unit of length used in the UK and the United States, 1 yard = 0.9144 metres.

==Transcript==
:[Cueball and Ponytail stand facing one another. Both hold sheets of paper. Cueball holds a restraining order, while Ponytail holds a map with two concentric circles drawn on it.]
:Not content with normal restraining orders, my ex got creative.
:Cueball: Wait... I can't get closer than 500 yards of you... or more than 600 yards away?
:Ponytail: You'll have to move somewhere within this ring.

{{comic discussion}}
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Ponytail]]
[[Category:Maps]]

1196: Subways

2016-10-01T23:21:28Z

162.158.255.64: /* Official subway maps */ Updated BART map link

{{comic
| number = 1196
| date = April 8, 2013
| title = Subways
| image = subways.png
| titletext = About one in three North American subway stops are in NYC.
}}
*The xkcd page links to [http://xkcd.com/1196/large/ a much larger version], which has another text added:
<blockquote style="font-style:italic">
For the pedantic rail enthusiasts, the definition of a subway used here is, with some caveats, "a network containing high capacity grade-separated passenger rail transit lines which run frequently, serve an urban core, and are underground or elevated for at least part of their downtown route." For the rest of you, the definition is "a bunch of trains under a city."
</blockquote>
{{TOC}}

==Explanation==
[[File:North American subways.svg.png|right|border|link=http://www.radicalcartography.net/subways.html|North America Subways by Prof. Bill Rankin]]
The comic shows the maps of all North American {{w|subway}} networks. In reality, none of these systems are interconnected, but in the diagram subways from different cities that have the same color on the official subway map have whimsically named connections, such as the "Ohio-California Tunnel" connecting the Green Lines of Cleveland and Los Angeles, or the "Rocky Mountain Tunnel" connecting the Blue Lines of Chicago and San Francisco. Vancouver and San Francisco are connected through a station called Richmond, which appears to double as {{w|Richmond, British Columbia}} and {{w|Richmond, California}}. The "Springfield Monorail" is fictional, from the animated series ''{{w|The Simpsons}}'' (see {{w|Marge vs. the Monorail}}), but its approximate location on this map would suggest the [http://www.seattlemonorail.com/ Seattle Monorail], or perhaps Springfield, Oregon, which [http://www.smithsonianmag.com/arts-culture/Matt-Groening-Reveals-the-Location-of-the-Real-Springfield.html Matt Groening revealed was the inspiration for the Simpsons' hometown].

The [http://www.radicalcartography.net/subways.html Urban Mass Transit Systems of North America] map (right) created by [http://hshm.yale.edu/rankin Yale Professor Bill Rankin] on his web site [http://www.radicalcartography.net/ Radical Cartography] in 2006 presents all of the subway systems in North America at the same scale using geographic, instead of topological, layout.

The networks on xkcd's map are displayed in (relatively) geographic position, with {{w|Vancouver}} being the most North-West, and {{w|Mexico City}} being the most South – East/West and North/South order are correct, but distances are not (in reality, Vancouver is closer to Chicago than to Toronto for example). The map's design is modeled after the system map of the {{w|Massachusetts Bay Transportation Authority}} in Boston where Randall is from.

===City-specific notes===

====Vancouver====
*The {{w|Canada Line}} and the {{w|Expo Line (TransLink)|Expo Line}} are shown as the same color; SkyTrain's official maps depict them with light blue and dark blue respectively.
*{{w|Richmond, British Columbia|Richmond}} is the name of the city where the southernmost terminus of the Canada Line is located, and shares its name with {{w|Richmond, California}} (see San Francisco section.)

====Boston====
*The "Green Line Extension to Canada" references {{w|Green Line Extension|the actual project}} to extend the {{w|Green Line (MBTA)|Green Line}} into Medford, north of Boston.
*The "Ashmont–Manhattan High-Speed Line" shown as connecting Boston's Red Line to New York City's 1 train is a play on the {{w|Ashmont-Mattapan High Speed Line}} in Boston.
*The {{w|Red Line (MBTA)|Red Line}} stops "Skinflower" and "Bonevine" are plays on the actual name of the Red Line's terminus, {{w|Braintree (MBTstation)|Braintree}}.

====San Francisco====
*Both Muni and BART are depicted in San Francisco's map and are completely separate systems, although the map gives the impression that trains interline between the two. Non-wheelchair-accessible stops on Muni lines are omitted.
*{{w|Richmond, California|Richmond}} is the name of the city where the northern terminus of the {{w|Richmond-Fremont line|Richmond–Fremont}} and the {{w|Richmond-Daly City/Millbrae line|Richmond–Daly City/Millbrae}} BART lines are located, and shares its name with {{w|Richmond, British Columbia|Richmond, British Columbia}} (see Vancouver section.)
*"Sunnydale" is the {{w|Sunnydale Station|actual name}} of the terminus of the Muni {{w|T Third Street}} line, not to be confused with {{w|Sunnydale|the city}} where ''Buffy the Vampire Slayer'' is set.

====Los Angeles====
*The {{w|Gold Line (Los Angeles Metro)|Gold Line}} and the {{w|Orange Line (Los Angeles Metro)|Orange Line}} are shown with swapped colors.
*The Orange Line is the only {{w|bus rapid transit}} (BRT) line to be shown on the map. LA Metro also operates a second BRT line, the {{w|Silver Line (Los Angeles Metro)|Silver Line}}, which is not shown.

====New York City====
*The {{w|New York City Subway}}, {{w|Port Authority Trans-Hudson}} (PATH), and the single line of the {{w|Staten Island Railway}} (with a connection via the {{w|Staten Island Ferry}}) are shown.
*{{w|Jamaica, Queens|Jamaica}} is the name of the neighborhood in Queens where the E, F, and J/Z trains terminate. Kingston is the capital and largest city in the country of Jamaica.
*The actual {{w|G (New York City Subway service)|G train}} is notorious for unreliable service, hence the "Random Service" notation.
*The "Robert Moses High-Speed Line" refers to the NYC urban planner {{w|Robert Moses}}, who was one of the most influential planners in supporting cars over all public transport, creating the car-dependent {{w|New York metropolitan area}}.

====Philadelphia====
*Both {{w|SEPTA}} subway lines, a portion of the {{w|SEPTA Subway–Surface Trolley Lines}}, and the {{w|PATCO Speedline}} are shown.
*"Trolley Rt. 10 to California" is a play on the actual {{w|SEPTA Route 10|Route 10}} trolley.

====Washington, DC====
*The "Graveyard for passengers killed by closing doors" refers to the warning played in the Washington DC Metro system advising passengers that the subway doors are "not like elevator doors" and will close on your limbs or belongings rather than opening when contact with an object is detected.
*The "Morgantown, WV Automated Line" references the {{w|Morgantown Personal Rapid Transit}} system, which was built in 1975 as a {{w|personal rapid transit}} demonstrator and serves the three campuses of West Virginia University.
*{{w|Greenbelt (WMATA station)|Greenbelt}} is the northern terminus of the Washington Metro's Green and Yellow lines, hence the Green line being depicted as forming a belt.
*This comic [http://globedigits.com/ website] was made before the Silver line was constructed, so it does not appear in the comic.

====Miami====
*The "Caribbean Metromover" references the {{w|Miami Metromover}}, a people mover in downtown Miami (not shown on the map.)
*The airport [https://www.logoventure.com/ logo] for Miami International Airport (MIA) is replaced with a [http://www.youtube.com/watch?v=ewRjZoRtu0Y paper airplane].

====San Juan====
*The "Puerto Rico Submarine" that connects the Red Lines of San Juan and New York refers to the fact that San Juan is on an island, namely {{w|Puerto Rico}}.
*The "Mona Tunnel" that connects the Red Lines of San Juan and Santo Domingo may refer to the island of {{w|Isla de Mona|Mona}}, which lies between Puerto Rico and Hispaniola.

====Monterrey====
*The "Chicxulub Tunnel" that connects the Red Lines of Santo Domingo and Monterey refers to the 65-million-year-old {{w|Chicxulub crater}}, which lies roughly between the two cities.

===Official subway maps===
*Atlanta - http://www.itsmarta.com/rail-schedules-or-route.aspx
*Baltimore (MTA Maryland) - http://mta.maryland.gov/sites/default/files/metro-subway.jpg
*Boston - http://www.mbta.com/schedules_and_maps/subway/
*Chicago (CTA) - http://www.transitchicago.com/assets/1/maps/P19_2012_CTA_Rail_Map.pdf
*Cleveland - http://www.riderta.com/pdf/maps/System_Map_Rapid_Connect.pdf
*Los Angeles (LACMTA) - http://www.metro.net/riding_metro/maps/images/rail_map.gif
*Mexico City - http://www.metro.df.gob.mx/imagenes/red/redinternet.pdf
*Montreal - http://www.stm.info/english/metro/images/plan-metro.jpg
*New York City (MTA) - http://www.mta.info/maps/submap.html
*New York City (PATH) - http://www.panynj.gov/path/maps.html
*Philadelphia (SEPTA and PATCO) - http://www.septa.org/maps/system/index.html
*San Francisco (BART) - http://www.bart.gov/sites/all/themes/bart_desktop/img/system-map.gif
*San Francisco (MUNI) - http://transit.511.org/static/providers/maps/SF_712200722845.gif
*Toronto (TTC) - https://www.tourbytransit.com/toronto/public-transit/subway
*Vancouver - http://mapa-metro.com/mapas/Vancouver/mapa-metro-vancouver.png
*Washington (WMATA) - http://wmata.com/rail/maps/map.cfm

{{clear}}

==Transcript==
:'''Subways of North America'''
:[A subway-line style (bold colored, 45-degree aligned lines with white bars indicating stations) map has been constructed by combining and linking various parts of the subway maps from many different cities, as if all of the transit systems were connected directly. The cities include (from top to bottom, left to right) Vancouver, Montreal, San Francisco, Toronto, Boston, Chicago, Los Angeles, Cleveland, New York City, Philadelphia, Baltimore, Washington DC, Miami, Atlanta, Monterrey, San Juan, Santo Domingo, and Mexico City.]

{{comic discussion}}

[[Category:Large drawings]]
[[Category:Comics with color]]
[[Category:Maps]]