https://www.explainxkcd.com/wiki/api.php?action=feedcontributions&user=172.68.226.16&feedformat=atomexplain xkcd - User contributions [en]2022-05-17T10:46:13ZUser contributionsMediaWiki 1.30.0https://www.explainxkcd.com/wiki/index.php?title=2295:_Garbage_Math&diff=1908942295: Garbage Math2020-04-18T12:50:51Z<p>172.68.226.16: /* Explanation */</p>
<hr />
<div>{{comic<br />
| number = 2295<br />
| date = April 17, 2020<br />
| title = Garbage Math<br />
| image = garbage_math.png<br />
| titletext = 'Garbage In, Garbage Out' should not be taken to imply any sort of conservation law limiting the amount of garbage produced.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Created by a ZILOG Z80. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}<br />
This comic explains the "{{w|garbage in, garbage out}}" concept using arithmetical expressions. Just like the comic says, if you get garbage in any part of your workflow, you get garbage as a result.<br />
<br />
Some of these rules correspond to the rules of {{w|floating point arithmetic}}, while others may be inspired by 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, and the uncertainty of the result of arithmetic operations will tend to be dominated by the term with the highest uncertainty. The rule about N pieces of independent garbage reflects the {{w|central limit theorem}} and how it predicts that the uncertainty (or {{w|standard error}}) of an estimate will be reduced when independent estimates are averaged. The comic oddly omits raising garbage to the 0th power, which transforms even NaN, the platonic ideal of garbage, to exactly 1.<br />
<br />
This comic is not related to the {{w|2019–20 coronavirus outbreak|2020 pandemic}} of the {{w|coronavirus}} {{w|SARS-CoV-2}}, which causes {{w|COVID-19}}, breaking the streak of comics preceding this on [[:Category:COVID-19|topics relating to COVID-19]], after (rather appropriately) 19 comics (not counting the [[2288: Collector's Edition|April Fools' comic]]).<br />
<br />
This comic is about the propagation of errors in numerical analysis and statistics, but described in much more colloquial terms. Numbers with low precision are termed "garbage" and numbers with high precision are labeled "precise".<br />
<br />
{| class="wikitable"<br />
!Formula<br />
!Statistical Expression<br />
!Explanation<br />
|-<br />
|Precise number + Precise number = Slightly less precise number<br />
|<math>\mathop\sigma(X+Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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<sup>-6</sup>) and 1 (±10<sup>-6</sup>), then our sum is 2 (±2·10<sup>-6</sup>). It is possible to lose a lot of relative precision, if the resultant sum is close to zero as a result of adding a number and then close to its inverse. This phenomenon is known as catastrophic cancellation. Therefore, it is likely that all numbers referred here are positive numbers, which does not exhibit this phenomenon.<br />
|-<br />
|Precise number × Precise number = Slightly less precise number<br />
|<math>\mathop\sigma(X\times Y)=\sqrt{(\mathop\sigma(X)\times Y)^2+(\mathop\sigma(Y)\times X)^2}</math><br />
|Here, instead of absolute error, relative error will be added. For example, if our precise numbers are 1 (±10<sup>-6</sup>) and 1 (±10<sup>-6</sup>), then our product is 1 (±2·10<sup>-6</sup>).<br />
|-<br />
|Precise number + Garbage = Garbage<br />
|<math>\mathop\sigma(X+Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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. <br />
|-<br />
|Precise number × Garbage = Garbage<br />
|<math>\mathop\sigma(X\times Y)=\sqrt{(\mathop\sigma(X)\times Y)^2+(\mathop\sigma(Y)\times X)^2}</math><br />
|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.<br />
|-<br />
|<math>\sqrt{\text{Garbage}} = \text{Less bad garbage}</math><br />
|<math>\mathop\sigma(\sqrt X)=\frac{\mathop\sigma(X)}{2\times\sqrt X} </math><br />
| 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''.<br />
|-<br />
|Garbage<sup>2</sup> = Worse garbage<br />
|<math>\mathop\sigma(X^2)=2\times X\times\mathop\sigma(X)</math><br />
|Likewise, when a number is squared, its relative error will be doubled. This is a corollary to multiplication adding relative errors.<br />
|-<br />
|<math>\frac{1}{N}\sum(\text{N pieces of statistically independent garbage}) = \text{Better garbage}</math><br />
|<br />
|By aggregating many pieces of statistically independent observations (for instance, surveying many individuals), it is possible to reduce relative error. This is the basis of statistical sampling.<br />
|-<br />
|Precise number<sup>Garbage</sup> = Much worse garbage<br />
|<math>\mathop\sigma(b^X)=b^{2\times X}\times\mathop{\mathrm{ln}}b\times\sigma(X)</math><br />
|The exponent is very sensitive to changes, which may also magnify the effect based on the magnitude of the precise number.<br />
|-<br />
|Garbage – Garbage = Much worse garbage<br />
|<math>\mathop\sigma(X-Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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.<br />
|-<br />
|<math>\frac{\text{Precise number}}{\text{Garbage}-\text{Garbage}}</math> = Much worse garbage, possible division by zero<br />
|<math>\mathop\sigma(\frac{X}{Y})=\sqrt{\frac{|(\mathop\sigma(X)\times Y)^2-(\mathop\sigma(Y)\times X)^2|}{\mathop\sigma(Y)}}</math><br />
|Indeed, as with above, if error bars overlap then we might end up dividing by zero.<br />
|-<br />
|Garbage × 0 = Precise number<br />
|<math>\mathop\sigma(0)=0</math><br />
|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.<br />
|}<br />
<br />
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.<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
<br />
[A series of mathematical equations are written from top to bottom]<br />
<br />
Precise number + Precise number = Slightly less precise number<br />
<br />
Precise number × Precise number = Slightly less precise number<br />
<br />
Precise number + Garbage = Garbage<br />
<br />
Precise number × Garbage = Garbage<br />
<br />
√<span style="border-top:1px solid; padding:0 0.1em;">Garbage</span> = Less bad garbage<br />
<br />
1/N Σ (N pieces of statistically independent garbage) = Better garbage<br />
<br />
(Precise number)<sup>Garbage</sup> = Much worse garbage<br />
<br />
Garbage – Garbage = Much worse garbage<br />
<br />
Precise number / ( Garbage – Garbage ) = Much worse garbage, possible division by zero<br />
<br />
Garbage × 0 = Precise number<br />
<br />
{{comic discussion}}<br />
[[Category:Math]]</div>172.68.226.16https://www.explainxkcd.com/wiki/index.php?title=2295:_Garbage_Math&diff=1908932295: Garbage Math2020-04-18T12:50:25Z<p>172.68.226.16: /* Explanation */</p>
<hr />
<div>{{comic<br />
| number = 2295<br />
| date = April 17, 2020<br />
| title = Garbage Math<br />
| image = garbage_math.png<br />
| titletext = 'Garbage In, Garbage Out' should not be taken to imply any sort of conservation law limiting the amount of garbage produced.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Created by a ZILOG Z80. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}<br />
This comic explains the "{{w|garbage in, garbage out}}" concept using arithmetical expressions. Just like the comic says, if you get garbage in any part of your workflow, you get garbage as a result.<br />
<br />
Some of these rules correspond to the rules of {{w|floating point arithmetic}}, while others may be inspired by 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, and the uncertainty of the result of arithmetic operations will tend to be dominated by the term with the highest uncertainty. The rule about N pieces of independent garbage reflects the {{w|central limit theorem}} and how it predicts that the uncertainty (or {{w|standard error}}) of an estimate will be reduced when independent estimates are averaged. The comic oddly omits raising garbage to the 0th power, which transforms even NaN, the platonic ideal of garbage, to exactly 1.<br />
<br />
This comic is not related to the {{w|2019–20 coronavirus outbreak|2020 pandemic}} of the {{w|coronavirus}} {{w|SARS-CoV-2}}, which causes {{w|COVID-19}}, breaking the streak of comics preceding this on [[:Category:COVID-19|topics relating to COVID-19]], after (rather appropriately) 19 comics (not counting the [[2288: Collector's Edition|April Fools' comic]]).<br />
<br />
This comic is about the propagation of errors in numerical analysis and statistics, but described in much more colloquial terms. Numbers with low precision are termed "garbage" and numbers with high precision are labeled "precise".<br />
<br />
{| class="wikitable"<br />
!Formula<br />
!Statistical Expression<br />
!Explanation<br />
|-<br />
|Precise number + Precise number = Slightly less precise number<br />
|<math>\mathop\sigma(X+Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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<sup>-6</sup>) and 1 (±10<sup>-6</sup>), then our sum is 2 (±2·10<sup>-6</sup>). It is possible to lose a lot of relative precision, if the resultant sum is close to zero as a result of adding a number and then close to its inverse. This phenomenon is known as catastrophic cancellation. Therefore, it is likely that all numbers referred here are positive numbers, which does not exhibit this phenomenon.<br />
|-<br />
|Precise number × Precise number = Slightly less precise number<br />
|<math>\mathop\sigma(X\times Y)=\sqrt{(\mathop\sigma(X)\times Y)^2+(\mathop\sigma(Y)\times X)^2}</math><br />
|Here, instead of absolute error, relative error will be added. For example, if our precise numbers are 1 (±10<sup>-6</sup>) and 1 (±10<sup>-6</sup>), then our product is 1 (±2·10<sup>-6</sup>).<br />
|-<br />
|Precise number + Garbage = Garbage<br />
|<math>\mathop\sigma(X+Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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. <br />
|-<br />
|Precise number × Garbage = Garbage<br />
|<math>\mathop\sigma(X\times Y)=\sqrt{(\mathop\sigma(X)\times Y)^2+(\mathop\sigma(Y)\times X)^2}</math><br />
|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.<br />
|-<br />
|<math>\sqrt{\text{Garbage}} = \text{Less bad garbage}</math><br />
|<math>\mathop\sigma(\sqrt X)=\frac{\mathop\sigma(X)}{2\times\sqrt X} </math><br />
| 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''.<br />
|-<br />
|Garbage<sup>2</sup> = Worse garbage<br />
|<math>\mathop\sigma(X^2)=2\times X\times\mathop\sigma(X)</math><br />
|Likewise, when a number is squared, its relative error will be doubled. This is a corollary to multiplication adding relative errors.<br />
|-<br />
|<math>\frac{1}{N}\sum(\text{N pieces of statistically independent garbage}) = \text{Better garbage}</math><br />
|<br />
|By aggregating many pieces of statistically independent observations (for instance, surveying many individuals), it is possible to reduce relative error. This is the basis of statistical sampling.<br />
|-<br />
|Precise number<sup>Garbage</sup> = Much worse garbage<br />
|<math>\mathop\sigma(b^X)=b^{2\times X}\times\mathop{\mathrm{ln}}b\times\sigma(X)</math><br />
|The exponent is very sensitive to changes, which may also magnify the effect based on the magnitude of the precise number.<br />
|-<br />
|Garbage – Garbage = Much worse garbage<br />
|<math>\mathop\sigma(X-Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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.<br />
|-<br />
|<math>\frac{\text{Precise number}}{\text{Garbage}-\text{Garbage}}</math> = Much worse garbage, possible division by zero<br />
|<math>\mathop\sigma(\frac{X}{Y})=\sqrt{frac{|(\mathop\sigma(X)\times Y)^2-(\mathop\sigma(Y)\times X)^2|}{\mathop\sigma(Y)}}</math><br />
|Indeed, as with above, if error bars overlap then we might end up dividing by zero.<br />
|-<br />
|Garbage × 0 = Precise number<br />
|<math>\mathop\sigma(0)=0</math><br />
|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.<br />
|}<br />
<br />
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.<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
<br />
[A series of mathematical equations are written from top to bottom]<br />
<br />
Precise number + Precise number = Slightly less precise number<br />
<br />
Precise number × Precise number = Slightly less precise number<br />
<br />
Precise number + Garbage = Garbage<br />
<br />
Precise number × Garbage = Garbage<br />
<br />
√<span style="border-top:1px solid; padding:0 0.1em;">Garbage</span> = Less bad garbage<br />
<br />
1/N Σ (N pieces of statistically independent garbage) = Better garbage<br />
<br />
(Precise number)<sup>Garbage</sup> = Much worse garbage<br />
<br />
Garbage – Garbage = Much worse garbage<br />
<br />
Precise number / ( Garbage – Garbage ) = Much worse garbage, possible division by zero<br />
<br />
Garbage × 0 = Precise number<br />
<br />
{{comic discussion}}<br />
[[Category:Math]]</div>172.68.226.16https://www.explainxkcd.com/wiki/index.php?title=2295:_Garbage_Math&diff=1908922295: Garbage Math2020-04-18T12:49:54Z<p>172.68.226.16: /* Explanation */</p>
<hr />
<div>{{comic<br />
| number = 2295<br />
| date = April 17, 2020<br />
| title = Garbage Math<br />
| image = garbage_math.png<br />
| titletext = 'Garbage In, Garbage Out' should not be taken to imply any sort of conservation law limiting the amount of garbage produced.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Created by a ZILOG Z80. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}<br />
This comic explains the "{{w|garbage in, garbage out}}" concept using arithmetical expressions. Just like the comic says, if you get garbage in any part of your workflow, you get garbage as a result.<br />
<br />
Some of these rules correspond to the rules of {{w|floating point arithmetic}}, while others may be inspired by 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, and the uncertainty of the result of arithmetic operations will tend to be dominated by the term with the highest uncertainty. The rule about N pieces of independent garbage reflects the {{w|central limit theorem}} and how it predicts that the uncertainty (or {{w|standard error}}) of an estimate will be reduced when independent estimates are averaged. The comic oddly omits raising garbage to the 0th power, which transforms even NaN, the platonic ideal of garbage, to exactly 1.<br />
<br />
This comic is not related to the {{w|2019–20 coronavirus outbreak|2020 pandemic}} of the {{w|coronavirus}} {{w|SARS-CoV-2}}, which causes {{w|COVID-19}}, breaking the streak of comics preceding this on [[:Category:COVID-19|topics relating to COVID-19]], after (rather appropriately) 19 comics (not counting the [[2288: Collector's Edition|April Fools' comic]]).<br />
<br />
This comic is about the propagation of errors in numerical analysis and statistics, but described in much more colloquial terms. Numbers with low precision are termed "garbage" and numbers with high precision are labeled "precise".<br />
<br />
{| class="wikitable"<br />
!Formula<br />
!Statistical Expression<br />
!Explanation<br />
|-<br />
|Precise number + Precise number = Slightly less precise number<br />
|<math>\mathop\sigma(X+Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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<sup>-6</sup>) and 1 (±10<sup>-6</sup>), then our sum is 2 (±2·10<sup>-6</sup>). It is possible to lose a lot of relative precision, if the resultant sum is close to zero as a result of adding a number and then close to its inverse. This phenomenon is known as catastrophic cancellation. Therefore, it is likely that all numbers referred here are positive numbers, which does not exhibit this phenomenon.<br />
|-<br />
|Precise number × Precise number = Slightly less precise number<br />
|<math>\mathop\sigma(X\times Y)=\sqrt{(\mathop\sigma(X)\times Y)^2+(\mathop\sigma(Y)\times X)^2}</math><br />
|Here, instead of absolute error, relative error will be added. For example, if our precise numbers are 1 (±10<sup>-6</sup>) and 1 (±10<sup>-6</sup>), then our product is 1 (±2·10<sup>-6</sup>).<br />
|-<br />
|Precise number + Garbage = Garbage<br />
|<math>\mathop\sigma(X+Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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. <br />
|-<br />
|Precise number × Garbage = Garbage<br />
|<math>\mathop\sigma(X\times Y)=\sqrt{(\mathop\sigma(X)\times Y)^2+(\mathop\sigma(Y)\times X)^2}</math><br />
|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.<br />
|-<br />
|<math>\sqrt{\text{Garbage}} = \text{Less bad garbage}</math><br />
|<math>\mathop\sigma(\sqrt X)=\frac{\mathop\sigma(X)}{2\times\sqrt X} </math><br />
| 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''.<br />
|-<br />
|Garbage<sup>2</sup> = Worse garbage<br />
|<math>\mathop\sigma(X^2)=2\times X\times\mathop\sigma(X)</math><br />
|Likewise, when a number is squared, its relative error will be doubled. This is a corollary to multiplication adding relative errors.<br />
|-<br />
|<math>\frac{1}{N}\sum(\text{N pieces of statistically independent garbage}) = \text{Better garbage}</math><br />
|<br />
|By aggregating many pieces of statistically independent observations (for instance, surveying many individuals), it is possible to reduce relative error. This is the basis of statistical sampling.<br />
|-<br />
|Precise number<sup>Garbage</sup> = Much worse garbage<br />
|<math>\mathop\sigma(b^X)=b^{2\times X}\times\mathop{\mathrm{ln}}b\times\sigma(X)</math><br />
|The exponent is very sensitive to changes, which may also magnify the effect based on the magnitude of the precise number.<br />
|-<br />
|Garbage – Garbage = Much worse garbage<br />
|<math>\mathop\sigma(X-Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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.<br />
|-<br />
|<math>\frac{\text{Precise number}}{\text{Garbage}-\text{Garbage}}</math> = Much worse garbage, possible division by zero<br />
|<math>\mathop\sigma(\frac{X}{Y})=\sqrt{frac{|(\mathop\sigma(X)\times Y)^2-(\mathop\sigma(Y)\times X)^2|}{\mathop\sigma(Y)}</math><br />
|Indeed, as with above, if error bars overlap then we might end up dividing by zero.<br />
|-<br />
|Garbage × 0 = Precise number<br />
|<math>\mathop\sigma(0)=0</math><br />
|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.<br />
|}<br />
<br />
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.<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
<br />
[A series of mathematical equations are written from top to bottom]<br />
<br />
Precise number + Precise number = Slightly less precise number<br />
<br />
Precise number × Precise number = Slightly less precise number<br />
<br />
Precise number + Garbage = Garbage<br />
<br />
Precise number × Garbage = Garbage<br />
<br />
√<span style="border-top:1px solid; padding:0 0.1em;">Garbage</span> = Less bad garbage<br />
<br />
1/N Σ (N pieces of statistically independent garbage) = Better garbage<br />
<br />
(Precise number)<sup>Garbage</sup> = Much worse garbage<br />
<br />
Garbage – Garbage = Much worse garbage<br />
<br />
Precise number / ( Garbage – Garbage ) = Much worse garbage, possible division by zero<br />
<br />
Garbage × 0 = Precise number<br />
<br />
{{comic discussion}}<br />
[[Category:Math]]</div>172.68.226.16https://www.explainxkcd.com/wiki/index.php?title=2295:_Garbage_Math&diff=1908912295: Garbage Math2020-04-18T12:49:31Z<p>172.68.226.16: /* Explanation */</p>
<hr />
<div>{{comic<br />
| number = 2295<br />
| date = April 17, 2020<br />
| title = Garbage Math<br />
| image = garbage_math.png<br />
| titletext = 'Garbage In, Garbage Out' should not be taken to imply any sort of conservation law limiting the amount of garbage produced.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Created by a ZILOG Z80. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}<br />
This comic explains the "{{w|garbage in, garbage out}}" concept using arithmetical expressions. Just like the comic says, if you get garbage in any part of your workflow, you get garbage as a result.<br />
<br />
Some of these rules correspond to the rules of {{w|floating point arithmetic}}, while others may be inspired by 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, and the uncertainty of the result of arithmetic operations will tend to be dominated by the term with the highest uncertainty. The rule about N pieces of independent garbage reflects the {{w|central limit theorem}} and how it predicts that the uncertainty (or {{w|standard error}}) of an estimate will be reduced when independent estimates are averaged. The comic oddly omits raising garbage to the 0th power, which transforms even NaN, the platonic ideal of garbage, to exactly 1.<br />
<br />
This comic is not related to the {{w|2019–20 coronavirus outbreak|2020 pandemic}} of the {{w|coronavirus}} {{w|SARS-CoV-2}}, which causes {{w|COVID-19}}, breaking the streak of comics preceding this on [[:Category:COVID-19|topics relating to COVID-19]], after (rather appropriately) 19 comics (not counting the [[2288: Collector's Edition|April Fools' comic]]).<br />
<br />
This comic is about the propagation of errors in numerical analysis and statistics, but described in much more colloquial terms. Numbers with low precision are termed "garbage" and numbers with high precision are labeled "precise".<br />
<br />
{| class="wikitable"<br />
!Formula<br />
!Statistical Expression<br />
!Explanation<br />
|-<br />
|Precise number + Precise number = Slightly less precise number<br />
|<math>\mathop\sigma(X+Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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<sup>-6</sup>) and 1 (±10<sup>-6</sup>), then our sum is 2 (±2·10<sup>-6</sup>). It is possible to lose a lot of relative precision, if the resultant sum is close to zero as a result of adding a number and then close to its inverse. This phenomenon is known as catastrophic cancellation. Therefore, it is likely that all numbers referred here are positive numbers, which does not exhibit this phenomenon.<br />
|-<br />
|Precise number × Precise number = Slightly less precise number<br />
|<math>\mathop\sigma(X\times Y)=\sqrt{(\mathop\sigma(X)\times Y)^2+(\mathop\sigma(Y)\times X)^2}</math><br />
|Here, instead of absolute error, relative error will be added. For example, if our precise numbers are 1 (±10<sup>-6</sup>) and 1 (±10<sup>-6</sup>), then our product is 1 (±2·10<sup>-6</sup>).<br />
|-<br />
|Precise number + Garbage = Garbage<br />
|<math>\mathop\sigma(X+Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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. <br />
|-<br />
|Precise number × Garbage = Garbage<br />
|<math>\mathop\sigma(X\times Y)=\sqrt{(\mathop\sigma(X)\times Y)^2+(\mathop\sigma(Y)\times X)^2}</math><br />
|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.<br />
|-<br />
|<math>\sqrt{\text{Garbage}} = \text{Less bad garbage}</math><br />
|<math>\mathop\sigma(\sqrt X)=\frac{\mathop\sigma(X)}{2\times\sqrt X} </math><br />
| 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''.<br />
|-<br />
|Garbage<sup>2</sup> = Worse garbage<br />
|<math>\mathop\sigma(X^2)=2\times X\times\mathop\sigma(X)</math><br />
|Likewise, when a number is squared, its relative error will be doubled. This is a corollary to multiplication adding relative errors.<br />
|-<br />
|<math>\frac{1}{N}\sum(\text{N pieces of statistically independent garbage}) = \text{Better garbage}</math><br />
|<br />
|By aggregating many pieces of statistically independent observations (for instance, surveying many individuals), it is possible to reduce relative error. This is the basis of statistical sampling.<br />
|-<br />
|Precise number<sup>Garbage</sup> = Much worse garbage<br />
|<math>\mathop\sigma(b^X)=b^{2\times X}\times\mathop{\mathrm{ln}}b\times\sigma(X)</math><br />
|The exponent is very sensitive to changes, which may also magnify the effect based on the magnitude of the precise number.<br />
|-<br />
|Garbage – Garbage = Much worse garbage<br />
|<math>\mathop\sigma(X-Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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.<br />
|-<br />
|<math>\frac{\text{Precise number}}{\text{Garbage}-\text{Garbage}}</math> = Much worse garbage, possible division by zero<br />
|<math>\mathop\sigma(\frac{X}{Y})=\sqrt{frac{|(\mathop\sigma(X)\times Y)^2-(\mathop\sigma(Y)\times X)^2|}\mathop\sigma(Y)}</math><br />
|Indeed, as with above, if error bars overlap then we might end up dividing by zero.<br />
|-<br />
|Garbage × 0 = Precise number<br />
|<math>\mathop\sigma(0)=0</math><br />
|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.<br />
|}<br />
<br />
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.<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
<br />
[A series of mathematical equations are written from top to bottom]<br />
<br />
Precise number + Precise number = Slightly less precise number<br />
<br />
Precise number × Precise number = Slightly less precise number<br />
<br />
Precise number + Garbage = Garbage<br />
<br />
Precise number × Garbage = Garbage<br />
<br />
√<span style="border-top:1px solid; padding:0 0.1em;">Garbage</span> = Less bad garbage<br />
<br />
1/N Σ (N pieces of statistically independent garbage) = Better garbage<br />
<br />
(Precise number)<sup>Garbage</sup> = Much worse garbage<br />
<br />
Garbage – Garbage = Much worse garbage<br />
<br />
Precise number / ( Garbage – Garbage ) = Much worse garbage, possible division by zero<br />
<br />
Garbage × 0 = Precise number<br />
<br />
{{comic discussion}}<br />
[[Category:Math]]</div>172.68.226.16https://www.explainxkcd.com/wiki/index.php?title=2295:_Garbage_Math&diff=1908902295: Garbage Math2020-04-18T12:47:18Z<p>172.68.226.16: /* Explanation */</p>
<hr />
<div>{{comic<br />
| number = 2295<br />
| date = April 17, 2020<br />
| title = Garbage Math<br />
| image = garbage_math.png<br />
| titletext = 'Garbage In, Garbage Out' should not be taken to imply any sort of conservation law limiting the amount of garbage produced.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Created by a ZILOG Z80. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}<br />
This comic explains the "{{w|garbage in, garbage out}}" concept using arithmetical expressions. Just like the comic says, if you get garbage in any part of your workflow, you get garbage as a result.<br />
<br />
Some of these rules correspond to the rules of {{w|floating point arithmetic}}, while others may be inspired by 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, and the uncertainty of the result of arithmetic operations will tend to be dominated by the term with the highest uncertainty. The rule about N pieces of independent garbage reflects the {{w|central limit theorem}} and how it predicts that the uncertainty (or {{w|standard error}}) of an estimate will be reduced when independent estimates are averaged. The comic oddly omits raising garbage to the 0th power, which transforms even NaN, the platonic ideal of garbage, to exactly 1.<br />
<br />
This comic is not related to the {{w|2019–20 coronavirus outbreak|2020 pandemic}} of the {{w|coronavirus}} {{w|SARS-CoV-2}}, which causes {{w|COVID-19}}, breaking the streak of comics preceding this on [[:Category:COVID-19|topics relating to COVID-19]], after (rather appropriately) 19 comics (not counting the [[2288: Collector's Edition|April Fools' comic]]).<br />
<br />
This comic is about the propagation of errors in numerical analysis and statistics, but described in much more colloquial terms. Numbers with low precision are termed "garbage" and numbers with high precision are labeled "precise".<br />
<br />
{| class="wikitable"<br />
!Formula<br />
!Statistical Expression<br />
!Explanation<br />
|-<br />
|Precise number + Precise number = Slightly less precise number<br />
|<math>\mathop\sigma(X+Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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<sup>-6</sup>) and 1 (±10<sup>-6</sup>), then our sum is 2 (±2·10<sup>-6</sup>). It is possible to lose a lot of relative precision, if the resultant sum is close to zero as a result of adding a number and then close to its inverse. This phenomenon is known as catastrophic cancellation. Therefore, it is likely that all numbers referred here are positive numbers, which does not exhibit this phenomenon.<br />
|-<br />
|Precise number × Precise number = Slightly less precise number<br />
|<math>\mathop\sigma(X\times Y)=\sqrt{(\mathop\sigma(X)\times Y)^2+(\mathop\sigma(Y)\times X)^2}</math><br />
|Here, instead of absolute error, relative error will be added. For example, if our precise numbers are 1 (±10<sup>-6</sup>) and 1 (±10<sup>-6</sup>), then our product is 1 (±2·10<sup>-6</sup>).<br />
|-<br />
|Precise number + Garbage = Garbage<br />
|<math>\mathop\sigma(X+Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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. <br />
|-<br />
|Precise number × Garbage = Garbage<br />
|<math>\mathop\sigma(X\times Y)=\sqrt{(\mathop\sigma(X)\times Y)^2+(\mathop\sigma(Y)\times X)^2}</math><br />
|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.<br />
|-<br />
|<math>\sqrt{\text{Garbage}} = \text{Less bad garbage}</math><br />
|<math>\mathop\sigma(\sqrt X)=\frac{\mathop\sigma(X)}{2\times\sqrt X} </math><br />
| 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''.<br />
|-<br />
|Garbage<sup>2</sup> = Worse garbage<br />
|<math>\mathop\sigma(X^2)=2\times X\times\mathop\sigma(X)</math><br />
|Likewise, when a number is squared, its relative error will be doubled. This is a corollary to multiplication adding relative errors.<br />
|-<br />
|<math>\frac{1}{N}\sum(\text{N pieces of statistically independent garbage}) = \text{Better garbage}</math><br />
|<br />
|By aggregating many pieces of statistically independent observations (for instance, surveying many individuals), it is possible to reduce relative error. This is the basis of statistical sampling.<br />
|-<br />
|Precise number<sup>Garbage</sup> = Much worse garbage<br />
|<math>\mathop\sigma(b^X)=b^{2\times X}\times\mathop{\mathrm{ln}}b\times\sigma(X)</math><br />
|The exponent is very sensitive to changes, which may also magnify the effect based on the magnitude of the precise number.<br />
|-<br />
|Garbage – Garbage = Much worse garbage<br />
|<math>\mathop\sigma(X-Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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.<br />
|-<br />
|<math>\frac{\text{Precise number}}{\text{Garbage}-\text{Garbage}}</math> = Much worse garbage, possible division by zero<br />
|<math>\mathop\sigma(\frac{X}{Y})=\sqrt{|(\mathop\sigma(X)\times Y)^2-(\mathop\sigma(Y)\times X)^2|}</math><br />
|Indeed, as with above, if error bars overlap then we might end up dividing by zero.<br />
|-<br />
|Garbage × 0 = Precise number<br />
|<math>\mathop\sigma(0)=0</math><br />
|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.<br />
|}<br />
<br />
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.<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
<br />
[A series of mathematical equations are written from top to bottom]<br />
<br />
Precise number + Precise number = Slightly less precise number<br />
<br />
Precise number × Precise number = Slightly less precise number<br />
<br />
Precise number + Garbage = Garbage<br />
<br />
Precise number × Garbage = Garbage<br />
<br />
√<span style="border-top:1px solid; padding:0 0.1em;">Garbage</span> = Less bad garbage<br />
<br />
1/N Σ (N pieces of statistically independent garbage) = Better garbage<br />
<br />
(Precise number)<sup>Garbage</sup> = Much worse garbage<br />
<br />
Garbage – Garbage = Much worse garbage<br />
<br />
Precise number / ( Garbage – Garbage ) = Much worse garbage, possible division by zero<br />
<br />
Garbage × 0 = Precise number<br />
<br />
{{comic discussion}}<br />
[[Category:Math]]</div>172.68.226.16https://www.explainxkcd.com/wiki/index.php?title=2295:_Garbage_Math&diff=1908892295: Garbage Math2020-04-18T12:35:52Z<p>172.68.226.16: /* Explanation */</p>
<hr />
<div>{{comic<br />
| number = 2295<br />
| date = April 17, 2020<br />
| title = Garbage Math<br />
| image = garbage_math.png<br />
| titletext = 'Garbage In, Garbage Out' should not be taken to imply any sort of conservation law limiting the amount of garbage produced.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Created by a ZILOG Z80. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}<br />
This comic explains the "{{w|garbage in, garbage out}}" concept using arithmetical expressions. Just like the comic says, if you get garbage in any part of your workflow, you get garbage as a result.<br />
<br />
Some of these rules correspond to the rules of {{w|floating point arithmetic}}, while others may be inspired by 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, and the uncertainty of the result of arithmetic operations will tend to be dominated by the term with the highest uncertainty. The rule about N pieces of independent garbage reflects the {{w|central limit theorem}} and how it predicts that the uncertainty (or {{w|standard error}}) of an estimate will be reduced when independent estimates are averaged. The comic oddly omits raising garbage to the 0th power, which transforms even NaN, the platonic ideal of garbage, to exactly 1.<br />
<br />
This comic is not related to the {{w|2019–20 coronavirus outbreak|2020 pandemic}} of the {{w|coronavirus}} {{w|SARS-CoV-2}}, which causes {{w|COVID-19}}, breaking the streak of comics preceding this on [[:Category:COVID-19|topics relating to COVID-19]], after (rather appropriately) 19 comics (not counting the [[2288: Collector's Edition|April Fools' comic]]).<br />
<br />
This comic is about the propagation of errors in numerical analysis and statistics, but described in much more colloquial terms. Numbers with low precision are termed "garbage" and numbers with high precision are labeled "precise".<br />
<br />
{| class="wikitable"<br />
!Formula<br />
!Statistical Expression<br />
!Explanation<br />
|-<br />
|Precise number + Precise number = Slightly less precise number<br />
|<math>\mathop\sigma(X+Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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<sup>-6</sup>) and 1 (±10<sup>-6</sup>), then our sum is 2 (±2·10<sup>-6</sup>). It is possible to lose a lot of relative precision, if the resultant sum is close to zero as a result of adding a number and then close to its inverse. This phenomenon is known as catastrophic cancellation. Therefore, it is likely that all numbers referred here are positive numbers, which does not exhibit this phenomenon.<br />
|-<br />
|Precise number × Precise number = Slightly less precise number<br />
|<math>\mathop\sigma(X\times Y)=\sqrt{(\mathop\sigma(X)\times Y)^2+(\mathop\sigma(Y)\times X)^2}</math><br />
|Here, instead of absolute error, relative error will be added. For example, if our precise numbers are 1 (±10<sup>-6</sup>) and 1 (±10<sup>-6</sup>), then our product is 1 (±2·10<sup>-6</sup>).<br />
|-<br />
|Precise number + Garbage = Garbage<br />
|<math>\mathop\sigma(X+Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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. <br />
|-<br />
|Precise number × Garbage = Garbage<br />
|<math>\mathop\sigma(X\times Y)=\sqrt{(\mathop\sigma(X)\times Y)^2+(\mathop\sigma(Y)\times X)^2}</math><br />
|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.<br />
|-<br />
|<math>\sqrt{\text{Garbage}} = \text{Less bad garbage}</math><br />
|<math>\mathop\sigma(\sqrt X)=\frac{\mathop\sigma(X)}{2\times\sqrt X} </math><br />
| 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''.<br />
|-<br />
|Garbage<sup>2</sup> = Worse garbage<br />
|<math>\mathop\sigma(X^2)=2\times X\times\mathop\sigma(X)</math><br />
|Likewise, when a number is squared, its relative error will be doubled. This is a corollary to multiplication adding relative errors.<br />
|-<br />
|<math>\frac{1}{N}\sum(\text{N pieces of statistically independent garbage}) = \text{Better garbage}</math><br />
|<br />
|By aggregating many pieces of statistically independent observations (for instance, surveying many individuals), it is possible to reduce relative error. This is the basis of statistical sampling.<br />
|-<br />
|Precise number<sup>Garbage</sup> = Much worse garbage<br />
|<math>\mathop\sigma(b^X)=b^{2\times X}\times\mathop{\mathrm{ln}}b\times\sigma(X)</math><br />
|The exponent is very sensitive to changes, which may also magnify the effect based on the magnitude of the precise number.<br />
|-<br />
|Garbage – Garbage = Much worse garbage<br />
|<math>\mathop\sigma(X-Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math><br />
|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.<br />
|-<br />
|<math>\frac{\text{Precise number}}{\text{Garbage}-\text{Garbage}}</math> = Much worse garbage, possible division by zero<br />
|<math>\mathop\sigma(\frac{X}{Y})=\sqrt{\mid{(\mathop\sigma(X)\times Y)^2-(\mathop\sigma(Y)\times X)^2}\mid}</math><br />
|Indeed, as with above, if error bars overlap then we might end up dividing by zero.<br />
|-<br />
|Garbage × 0 = Precise number<br />
|<math>\mathop\sigma(0)=0</math><br />
|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.<br />
|}<br />
<br />
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.<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
<br />
[A series of mathematical equations are written from top to bottom]<br />
<br />
Precise number + Precise number = Slightly less precise number<br />
<br />
Precise number × Precise number = Slightly less precise number<br />
<br />
Precise number + Garbage = Garbage<br />
<br />
Precise number × Garbage = Garbage<br />
<br />
√<span style="border-top:1px solid; padding:0 0.1em;">Garbage</span> = Less bad garbage<br />
<br />
1/N Σ (N pieces of statistically independent garbage) = Better garbage<br />
<br />
(Precise number)<sup>Garbage</sup> = Much worse garbage<br />
<br />
Garbage – Garbage = Much worse garbage<br />
<br />
Precise number / ( Garbage – Garbage ) = Much worse garbage, possible division by zero<br />
<br />
Garbage × 0 = Precise number<br />
<br />
{{comic discussion}}<br />
[[Category:Math]]</div>172.68.226.16https://www.explainxkcd.com/wiki/index.php?title=1132:_Frequentists_vs._Bayesians&diff=1839811132: Frequentists vs. Bayesians2019-12-02T13:09:34Z<p>172.68.226.16: /* Trivia */ fixed supernova explanation - previous wording was wrong</p>
<hr />
<div>{{comic<br />
| number = 1132<br />
| date = November 9, 2012<br />
| title = Frequentists vs. Bayesians<br />
| image = frequentists_vs_bayesians.png<br />
| titletext = 'Detector! What would the Bayesian statistician say if I asked him whether the--' [roll] 'I AM A NEUTRINO DETECTOR, NOT A LABYRINTH GUARD. SERIOUSLY, DID YOUR BRAIN FALL OUT?' [roll] '... yes.'}}<br />
<br />
==Explanation==<br />
This comic is a joke about jumping to conclusions based on a simplistic understanding of probability. The "{{w|base rate fallacy}}" is a mistake where an unlikely explanation is dismissed, even though the alternative is even less likely. In the comic, a device tests for the (highly unlikely) event that the sun has exploded. A degree of random error is introduced, by rolling two {{w|dice}} and lying if the result is double sixes. Double sixes are unlikely (1 in 36, or about 3% likely), so the statistician on the left dismisses it. The statistician on the right has (we assume) correctly reasoned that the sun exploding is ''far more'' unlikely, and so is willing to stake money on his interpretation.<br />
<br />
The labels given to the two statisticians, in their panels and in the comic's title, are not particularly fair or accurate, a fact which [[Randall]] has acknowledged:<ref name="munroe-on-gelman">[http://web.archive.org/web/20130117080920/http://andrewgelman.com/2012/11/16808/#comment-109366 Comment by Randall Munroe] to "I don’t like this cartoon", blog post by Andrew Gelman in ''Statistical Modeling, Causal Inference, and Social Science''. Archived Jan 17 2013 by the Wayback Machine.</ref><br />
<blockquote>I seem to have stepped on a hornet’s nest, though, by adding “Frequentist” and “Bayesian” titles to the panels. This came as a surprise to me, in part because I actually added them as an afterthought, along with the final punchline. … The truth is, I genuinely didn’t realize Frequentists and Bayesians were actual camps of people—all of whom are now emailing me. I thought they were loosely-applied labels—perhaps just labels appropriated by the books I had happened to read recently—for the standard textbook approach we learned in science class versus an approach which more carefully incorporates the ideas of prior probabilities.</blockquote><br />
<br />
The "frequentist" statistician is (mis)applying the common standard of "{{w|P-value|p}}<0.05". In a scientific study, a result is presumed to provide strong evidence if, given that the {{w|null hypothesis}}, a default position that the observations are unrelated (in this case, that the sun has ''not'' gone nova), there is less than a 5% chance that the result was merely random. (The null hypothesis was also referenced in [[892: Null Hypothesis]].)<br />
<br />
Since the likelihood of rolling double sixes is below this 5% threshold, the "frequentist" decides (by this rule of thumb) to accept the detector's output as correct. The "Bayesian" statistician has, instead, applied at least a small measure of probabilistic reasoning ({{w|Bayesian inference}}) to determine that the unlikeliness of the detector lying is greatly outweighed by the unlikeliness of the sun exploding. Therefore, he concludes that the sun has ''not'' exploded and the detector is lying.<br />
<br />
The line, "Bet you $50 it hasn't", is a reference to the approach of a leading Bayesian scholar, {{w|Bruno de Finetti}}, who made extensive use of bets in his examples and thought experiments. See {{w|Coherence (philosophical gambling strategy)}} for more information on his work. In this case, however, the bet is also a joke because we would all be dead if the sun exploded. If the Bayesian wins the bet, he gets money, and if he loses, they'll both be dead before money can be paid. This underlines the absurdity of the premise and emphasizes the need to consider context when examining probability.<br />
<br />
The title text refers to a classic series of logic puzzles known as {{w|Knights and Knaves#Fork in the road|Knights and Knaves}}, where there are two guards in front of two exit doors, one of which is real and the other leads to death. One guard is a liar and the other tells the truth. The visitor doesn't know which is which, and is allowed to ask one question to one guard. The solution is to ask either guard what the other one would say is the real exit, then choose the opposite. Two such guards were featured in the 1986 Jim Henson movie ''{{w|Labyrinth (1986 film)|Labyrinth}}'', hence the mention of "A LABYRINTH GUARD" here. A labyrinth was also mentioned in [[246: Labyrinth Puzzle]].<br />
<br />
===Further a less serious mathematical exploration===<br />
As mentioned, this is an instance of the {{w|base rate fallacy}}. If we treat the "truth or lie" setup as simply modelling an inaccurate test, then it is also specifically an illustration of the {{w|false positive paradox}}: A test that is rarely wrong, but which tests for an event that is even rarer, will be more often wrong than right when it says that the event has occurred.<br />
<br />
The test, in this case, is a neutrino detector. It relies on the fact that neutrinos can pass through the earth, so a neutrino detector would detect neutrinos from the sun at all times, day and night. The detector is stated to give false results ("lie") 1/36th of the time.<br />
<br />
There is no record of any star ever spontaneously exploding—they always show signs of deterioration long before their explosion—so the probability is near zero. For the sake of a number, though, consider that the sun's estimated lifespan is 10 billion years. Let's say the test is run every hour, twelve hours a day (at night time). This gives us a probability of the Sun exploding at one in 4.38×10<sup>13</sup>. Assuming this detector is otherwise reliable, when the detector reports a solar explosion, there are two possibilities:<br />
# The sun '''has''' exploded (one in 4.38×10<sup>13</sup>) and the detector '''is''' telling the truth (35 in 36). This event has a total probability of about 1/(4.38×10<sup>13</sup>) × 35/36 or about one in 4.50×10<sup>13</sup>.<br />
# The sun '''hasn't''' exploded (4.38×10<sup>13</sup> − 1 in 4.38×10<sup>13</sup>) and the detector '''is not''' telling the truth (1 in 36). This event has a total probability of about (4.38×10<sup>13</sup> − 1) / 4.38×10<sup>13</sup> × 1/36 or about one in 36.<br />
<br />
Clearly the sun exploding is not the most likely option. Indeed, Bayes' theorem can be used to find the probability that the Sun has exploded, given a result of "yes" and the prior probability given above:<br />
<br />
: <math><br />
\begin{align}<br />
P(\text{exploded}\,|\,\text{yes})&=\frac{P(\text{yes}\,|\,\text{exploded})P(\text{exploded})}{P(\text{yes})}\\<br />
&=\frac{P(\text{exploded})(1-P(\text{lie}))}{P(\text{exploded})(1-P(\text{lie}))+P(\text{lie})(1-P(\text{exploded}))}\\<br />
&\approx\frac1{1.25226\times10^{12}}<br />
\end{align}<br />
</math><br />
<br />
==Transcript==<br />
:Did the sun just explode? (It's night, so we're not sure)<br />
<br />
:[Two statisticians stand alongside an adorable little computer that is suspiciously similar to K-9 that speaks in Westminster typeface.]<br />
:Frequentist Statistician: This neutrino detector measures whether the sun has gone nova.<br />
:Bayesian Statistician: Then, it rolls two dice. If they both come up as six, it lies to us. Otherwise, it tells the truth.<br />
:Frequentist Statistician: Let's try. [to the detector] Detector! Has the sun gone nova?<br />
:Detector: ''roll'' YES.<br />
<br />
:Frequentist Statistician:<br />
:Frequentist Statistician: The probability of this result happening by chance is 1/36=0.027. Since p<0.05, I conclude that the sun has exploded.<br />
<br />
:Bayesian Statistician:<br />
:Bayesian Statistician: Bet you $50 it hasn't.<br />
<br />
==Trivia==<br />
* The Sun will never explode as a supernova, because it does not have enough mass to undergo core collapse and also does not have a companion star<br />
*In the same blog comment as cited above<ref name="munroe-on-gelman"/>, Randall explains that he chose the "sun exploding" scenario as a more clearly absurd example than those usually used:<br />
<blockquote>…I realized that in the common examples used to illustrate this sort of error, like the cancer screening/drug test false positive ones, the correct result is surprising or unintuitive. So I came up with the sun-explosion example, to illustrate a case where naïve application of that significance test can give a result that’s obviously nonsense.</blockquote><br />
*"Bayesian" statistics is named for Thomas Bayes, who studied conditional probability — the likelihood that one event is true when given information about some other related event. From {{w|Bayes Theorem|Wikipedia}}: "Bayesian interpretation expresses how a subjective degree of belief should rationally change to account for evidence".<br />
* The "frequentist" says that 1/36 = 0.027. It's actually 0.02777…, which should round to 0.028.<br />
* Using neutrino detectors to get an advance warning of a supernova is possible, and the {{w|Supernova Early Warning System}} does just this. The neutrinos arrive ahead of the photons, because they can escape from the core of the star before the supernova explosion reaches the mantle.<br />
<br />
==References==<br />
<references/><br />
<br />
{{comic discussion}}<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Multiple Cueballs]]<br />
[[Category:Statistics]]<br />
[[Category:Physics]]</div>172.68.226.16https://www.explainxkcd.com/wiki/index.php?title=Talk:2220:_Imagine_Going_Back_in_Time&diff=181955Talk:2220: Imagine Going Back in Time2019-10-30T10:19:45Z<p>172.68.226.16: </p>
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<div><!--Please sign your posts with ~~~~ and don't delete this text. New comments should be added at the bottom.--><br />
I wonder if Randall had a particular "frog pokemon" in mind? Croagunk, Toxicroak, Froakie, Frogadier, Greninja...? [[Special:Contributions/172.69.44.150|172.69.44.150]] 19:58, 25 October 2019 (UTC)<br />
:Hint: First, Pokemon Go didn't finished deploying generation 5 pokemons yet. Second, Trump is totally toxic. -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 23:17, 25 October 2019 (UTC)<br />
::The Poliwhirl family dates from Generation 1 and is the "original" frog pokémon. --[[Special:Contributions/162.158.122.36|162.158.122.36]] 23:59, 25 October 2019 (UTC)<br />
:::Yes so fur sure the frog Pokémon Politoed from gen 2, since the Poliwag is tadpoles. I agree that Toxicroach or Croagunk would fit better with Trump in Randall's view, but it is a reelect Trump fan, so he would most likely use a green frog that is not "ugly". Have added this to the description with link to page with picture. --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 22:08, 26 October 2019 (UTC)<br />
::::Agree that Politoed is the most likely, but contrary to what the page says currently, croagunk and toxicroak have been in the game for a few months now. (I just had a bunch of croagunk in my area and evolved a toxicroak, which is why I had them in mind when I made my previous comment.)[[Special:Contributions/172.69.44.150|172.69.44.150]] 20:13, 28 October 2019 (UTC)<br />
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<br />
"... and I suppose Marla Maples is the first lady!" [[Special:Contributions/172.68.38.88|172.68.38.88]] 20:04, 25 October 2019 (UTC)<br />
I know that Randall, and by extension Cueball, are not enthusiastic about the idea of dealing with a player who goes by "Reelect Trump 2020", but what does it mean that there is a frog Pokemon in the gym alongside? In other words, is Cueball's annoyance just that there is a Trump-promoting player in the game or is there more to it than that? --[[Special:Contributions/172.69.90.46|172.69.90.46]] 20:16, 25 October 2019 (UTC)<br />
:I see that at least you made the connection to the original "Back to the Future" when Marty meets Doc in 1955 and tells him that Ronald Reagan is President. [[User:RAGBRAIvet|RAGBRAIvet]] ([[User talk:RAGBRAIvet|talk]]) 06:04, 28 October 2019 (UTC)<br />
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:Definitely the Trump-promoting, as Toxicroak wouldn't be that hard pokemon to remove, with max CP 2488. Wait, "next to mine"? Ok, so he plays same team as Cueball and Cueball CANT remove it due to that. -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 23:17, 25 October 2019 (UTC)<br />
::And it is not a toxic pokémon when it is a fan of Trump that put it in! See above. --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 22:08, 26 October 2019 (UTC)<br />
<br />
:The frog Pokemon is likely a reference to Pepe the Frog, which is a meme popular with Trump supporters--[[Special:Contributions/172.68.90.112|172.68.90.112]] 20:52, 25 October 2019 (UTC)<br />
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Trump was quite sufficiently (in)famous by 1999. Remember that he divorced his most famous wife, Ivana, in 1991. His various business and romantic <s>failures</s> ventures were regular tabloid fodder throughout the 90s. If you think a 1999 person would have never heard of Trump, you're obviously <s>too young to be using the internet</s> younger than I am. I think the main joke in this comic is that Cueball goes back expecting his younger self to go, "wait, re-elect WHO??", but his younger self doesn't even bat an eyelash at that part. [[Special:Contributions/173.245.52.175|173.245.52.175]] 21:03, 25 October 2019 (UTC)<br />
:Famous, yes. Expected to became president, no. And young Cueball might be too young to care about tabloids and celebrities. -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 23:17, 25 October 2019 (UTC)<br />
:Nobody - not even Randall - is suggesting ANYBODY didn't know who Trump was in 1999. He's been quite famous for decades. The surprise here is that he's president, not who he is. [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 03:29, 26 October 2019 (UTC)<br />
:He was famous enough to be a recognizable cameo in ''Home Alone 2'' with no explanation (and ''Home Alone 2'' was basically ''the'' holiday movie at the time, since no one liked ''Home Alone 3''), but that fame was nothing compared to how famous he'd become later--[[Special:Contributions/162.158.122.36|162.158.122.36]] 15:07, 27 October 2019 (UTC)<br />
::There is a ''Home Alone 3''? oO [[User:Elektrizikekswerk|Elektrizikekswerk]] ([[User talk:Elektrizikekswerk|talk]]) 14:05, 28 October 2019 (UTC)<br />
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Has no one considered that we have been "dumbed down" to the point that so-called adults playing Pokemon and so-called adults voting for Trump are inextricably linked and are symptoms of the same malaise - a general inability to think for ourselves and a deep susceptibility to marketing, advertising and following the herd[[Special:Contributions/108.162.241.148|108.162.241.148]] 03:05, 26 October 2019 (UTC)<br />
:Yes, but nobody important. [[Special:Contributions/172.69.34.98|172.69.34.98]] 03:11, 26 October 2019 (UTC)<br />
::Adults playing Pokemon just means they’re happy doing what makes them happy, why should someone be ashamed of it? [[Special:Contributions/162.158.166.141|162.158.166.141]] 10:35, 26 October 2019 (UTC)<br />
:::Yes, I play Pokémon Go, I'm in my forties, and most of the other players I play with are adults although here it has had a revive with the kids in school again. I get a lot of fresh air and more exercise than I got before starting to play 2,5 year ago. And with Randall's obsession with Pokémon and his knowledge about the games mechanics he most likely plays it himself. There are millions of adults playing every day as it is one of the most downloaded apps in app store. --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 22:08, 26 October 2019 (UTC) <br />
:::If *children* are mocking you for being childish, you *should* probably sit down and think about it for a moment. The thought seems to have struck Randall, too. --[[Special:Contributions/162.158.90.66|162.158.90.66]] 21:58, 28 October 2019 (UTC)<br />
<br />
Just as I remember reading in a 1969 textbook that Ronald Regan was going to someday be elected President if (then current) political trends that became the “southern strategy” weren’t addressed, I also remember reading at least one op-Ed piece in the late 1990’s that if the political parties didn’t clean house and get rid of undue influence from big donors that someday Donald Trump would become President. There were people worried about Trump in 1999.[[Special:Contributions/162.158.62.129|162.158.62.129]] 04:13, 26 October 2019 (UTC)<br />
<br />
I can't help but wonder if the wording of the title text is meant to invoke another shocking reveal when considering what "trendy adults" really are into these days.--[[User:Henke37|Henke37]] ([[User talk:Henke37|talk]]) 15:30, 26 October 2019 (UTC)<br />
<br />
What's with the width of this comic? It's too wide, and it breaks out of the standard xkcd.com layout a little bit. --[[User:NeatNit|NeatNit]] ([[User talk:NeatNit|talk]]) 16:31, 27 October 2019 (UTC)<br />
:I noticed this, too. Has this happened before? -- [[User:Dtgriscom|Dtgriscom]] ([[User talk:Dtgriscom|talk]]) 14:47, 28 October 2019 (UTC)<br />
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20 years ago, I was a whiny little shit and would have probably ranted that I'm to cool for Pokemon, instead of just admitting that it looks interesting and would have wanted a gameboy to play it myself. [[Special:Contributions/172.69.55.22|172.69.55.22]] 10:10, 28 October 2019 (UTC)<br />
<br />
I am not sure which I find more disturbing. Randall's apparent unthinking Trump Derangement Syndrome (I would have imagined him too intelligent to fall for mere politics) or the fact that Explain XKCD seems to have been invaded by Goldman Sachs advertising. If you are going to use an ad rotator, could you at least set it to display DIFFERENT adverts on the same page? I don't need to see the same advert 3 times. [[User:Seebert|Seebert]] ([[User talk:Seebert|talk]]) 12:55, 28 October 2019 (UTC)<br />
:In all fairness, I must point out that it is ''Cueball'' giving an kneejerk anti-Trump reaction in this comic, not Randall himself. While Randall does often project his own views through the characters of his comic, we cannot say for certain that that is the case here. In the past he has often created characters with incorrect or strawman positions in order to make a point or to satirize them. [[User:Hawthorn|Hawthorn]] ([[User talk:Hawthorn|talk]]) 13:46, 28 October 2019 (UTC)<br />
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Hmm, It seems to me that today's Cueball's (TP) dismay with the past's Cueball's (PC) reaction isn't about Trump, it's about calling him old and questioning his continued Pokemon-ing. This seems more in line with my impression of his priorities in life. With the two of them together, they could easily lose track of the 2nd half of the original odd statement and go off on the "what are you saying about me?" tangent - which makes the "I didn't come here to be mocked!" make a little more narrative sense. PC doesn't show any interesting in the Trump aspect, merely the idea of TP's still playing and being 20 years older, seems to be worth his consideration. I don't see it as changing the future sort of thing, don't you have to kill your grandfather or something to do that? [[User:Afbach|Afbach]] ([[User talk:Afbach|talk]])<br />
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I had the feeling that old Cueball dies/disappears, because young one decides not to do childish things at age 40, altering the future. [[Special:Contributions/172.68.226.16|172.68.226.16]] 10:19, 30 October 2019 (UTC)<br />
<br />
== Google ads ==<br />
<br />
[[File:explainxkcd ads.jpg|thumb|100px]] When looking at the article page, I'm seeing several Google ads splashed across the full width of the article space, breaking it up randomly and making it more difficult to read (it sometimes interrupts the Transcript, for example, and also randomly crops up in the already-hard-to-read Discussion box). It looks awful. Is anyone else seeing them? I understand that ads are needed to pay for Explain XKCD's server costs, but they're really detrimental to the article. [[User:Hawthorn|Hawthorn]] ([[User talk:Hawthorn|talk]]) 13:13, 28 October 2019 (UTC)<br />
: Yeah, I'm seeing them, too, and I agree. ExplainXKCD is one of the few pages on my AdBlock white list. Please don't make me reconsider my decision. [[User:Elektrizikekswerk|Elektrizikekswerk]] ([[User talk:Elektrizikekswerk|talk]]) 13:47, 28 October 2019 (UTC)<br />
: Thank you for creating the new section. Yes, not only am I seeing them invade the text, but invade the text three times with the same advert. Perhaps we need a new tag to make room for advertising [[Special:Contributions/172.68.174.22|172.68.174.22]] 13:59, 28 October 2019 (UTC)<br />
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: I've added a tall screenshot of this to the right. Just from the thumbnail it's easy to see how disruptive it is to the page. --[[User:NeatNit|NeatNit]] ([[User talk:NeatNit|talk]]) 21:06, 28 October 2019 (UTC)<br />
::Oh, yours have images? Mine don't - they're just big white blocks with some text in them (which I think is even ''more'' disruptive since they are harder to distinguish from body text). But still, yeah, absolutely not a fan of this at all. It makes the site feel incredibly tacky. [[User:Hawthorn|Hawthorn]] ([[User talk:Hawthorn|talk]]) 21:34, 28 October 2019 (UTC)<br />
:::Yes I also see them with pictures and it is horrible. :-( Will try to see if making a [[explain_xkcd:Community_portal/Admin_requests#Google_ads_all_over_the_text|Admin requests]] will help... --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 10:34, 29 October 2019 (UTC)<br />
:I'm only seeing 1 ad, always (regardless of which comic's explanation I'm seeing) after the second paragraph, always with pictures. The existence of the ad doesn't annoy me as much as the fact that it'll sometimes load after I've already read past that point, pushing the text I ''am'' reading down. --[[Special:Contributions/162.158.123.103|162.158.123.103]] 16:47, 29 October 2019 (UTC)</div>172.68.226.16https://www.explainxkcd.com/wiki/index.php?title=2210:_College_Athletes&diff=1808792210: College Athletes2019-10-04T21:44:40Z<p>172.68.226.16: Undo revision 180828 by 172.68.189.19 (talk) That asterisk is not unnecessary.</p>
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<div>{{comic<br />
| number = 2210<br />
| date = October 2, 2019<br />
| title = College Athletes<br />
| image = college_athletes.png<br />
| titletext = Their signature play is the three-point combinator, a recursive offense which is guaranteed not to halt and continues accumulating points until the buzzer.<br />
}}<br />
<br />
==Explanation==<br />
[[Ponytail]] is reading from her phone about the [https://www.nytimes.com/2019/09/30/sports/college-athletes-paid-california.html California Fair Pay to Play act], which was signed into law on September 30, 2019, two days before this comic was released. It gives college athletes the rights to their name and image (face, body, etc.) for financial gain, in contrast to {{w|NCAA}} rules which require that athletes be unpaid. This bill threatens {{w|Amateurism in the NCAA|the NCAA's notion of amateurism}}, which has become a topic of public debate.<br />
<br />
[[White Hat]] thinks this law is a good thing, but then [[Cueball]] claims that his state has passed an even better law giving college players rights to the names and images of ''any'' California athletes. Note that Cueball's state is thus not California, so it is very odd they can use names from another state, in addition to the oddity of gaining rights to another person's name and image.<br />
<br />
Ponytail doesn't believe Cueball, but he carries on claiming that all members of his school's basketball team thus have changed their name to {{w|Steph Curry}} after the NBA player who plays for the {{w|Golden State Warriors}}, a team in California. Cueball explains in particular that only one player copied the name from the NBA player, then another member of the team copied the name from that player, and so on. <br />
<br />
As it turns out, in his final remark, all this has only been the setup for his grand joke: Cueball tells Ponytail and White Hat that this process of recursive name usage is known as "currying". In addition to a pun with basketball rules against ''carrying'', avoidance of which often involves passing from one player to another, this is also a play on both the basketball player's name "Curry" used here, as well as the mathematical procedure called {{w|currying}}, named after mathematician {{w|Haskell Curry}}. This sort of humor is very typical of Cueball, leading Ponytail to state that she "hates him".<br />
<br />
Currying is when a multi-variable function is broken down into a sequence of single-variable functions, each of which outputs a new function until the final variable is consumed. For example, the function f(x,y,z) can be curried into f(x)(y)(z), where f is a function that consumes x and produces a function f(x), which in turn consumes y, yielding the function f(x)(y), and that in turn is a function f(x)(y) which consumes the parameter z to finally produce f(x)(y)(z), which is equal to the original f(x,y,z). This is not commonly used in most areas of math except for foundational logic but it is widely used in functional programming.<br />
<br />
When Cueball says ''a team made up entirely of Steph Currys'', White Hat questions what the plural form should be, and should it instead have been "''Stephs Curry''"? This is referring to the pluralization of phrases where a noun is followed by a modifier of some sort, such as ''attorneys general'', ''parts unknown'', ''heirs apparent'', ''mothers-in-law'', and so on. In these cases, plurals are formed by pluralizing the noun parts of the phrases; however, some of these are rare or foreign enough that speakers of English don't always identify them correctly and pluralize the last word instead, e.g. *''attorney generals''.<br />
<br />
The title text is a computer science joke, saying that the Steph Currys basketball team's signature play is the "three-point combinator", a joke on the {{w|three-point play}} in basketball, and a type of {{w|Fixed-point_combinator#Y_combinator|fixed-point combinator}} called the [https://rosettacode.org/wiki/Y_combinator Y Combinator], introduced by Haskell Curry. The description of "three-point combinator" is dense with word play that relates to the Y Combinator, which is used to implement {{w|recursive}} methods in functional programming languages, has notable properties relating to halting (see: the {{w|halting problem}}), and has a common form in which a second argument is used as a counter that is increased by one with each recursive call until termination. "Signature play" may also be a play on words, as currying transforms a {{w|Type_signature#Method_signature|method signature}}.<br />
<br />
In this case, when this move is performed, it will just keep accumulating points, as it is guaranteed it cannot halt and will not stop until the time runs out and the buzzer that ends the game is activated. Such a move can of course not be a part of a real basketball game, and more of a nod to the Golden State Warriors' reputation as a high-scoring, nearly-unstoppable offense widely known for three-point shooting.<br />
<br />
==Transcript==<br />
:[Cueball, Ponytail and White Hat are having a conversation. Ponytail is checking her phone.]<br />
:Ponytail: Oh, huh. California passed a law giving college athletes full rights to their names and images.<br />
:White Hat: Good, I think?<br />
<br />
:[Cueball holds his hand up in a fist, while Ponytail, holding her phone down, and White Hat looks at him.]<br />
:Cueball: That's nothing. '''''Our''''' state gave college players rights to use the names and images of '''''any''''' California athletes.<br />
:Ponytail: It did not.<br />
<br />
:[In a frame-less panel Cueball holds his hands out, Ponytail's phone is gone and White Hat puts a hand to his chin.]<br />
:Cueball: Sure it did!<br />
:Cueball: That's how our school fielded a basketball team made up entirely of Steph Currys.<br />
:White Hat: Or is the plural "Stephs Curry"?<br />
<br />
:[Cueball holds both hands up in front of him. Ponytail has her arms down but she is balling her hands into fists.]<br />
:Cueball: They didn't all copy the original Steph, though. One player got the rights to his name, then the next player got it from them, and so on.<br />
:Cueball: This process is known as "currying".<br />
:Ponytail: ...I hate you so much.<br />
<br />
{{comic discussion}}<br />
<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Comics featuring Ponytail]]<br />
[[Category:Comics featuring White Hat]]<br />
[[Category:Comics featuring real people]]<br />
[[Category:Sport]] <!-- Athletes is not just Basketball! So inserted this category again--><br />
[[Category:Basketball]]<br />
[[Category:Math]]<br />
[[Category:Programming]]</div>172.68.226.16https://www.explainxkcd.com/wiki/index.php?title=Talk:2034:_Equations&diff=161402Talk:2034: Equations2018-08-17T16:50:32Z<p>172.68.226.16: ;Gauge theory equation :I think the transcript is missing a left superscript 0 before the turned xi.</p>
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<div><!--Please sign your posts with ~~~~ and don't delete this text. New comments should be added at the bottom.--><br />
Is the joke that all of the equations are actually wrong/malformed/meaningless but they sort of look like typical equations for that field? {{unsigned ip|172.68.133.66}}<br />
:Sort of. A bit of dimensional analysis would have helped. ;-) --[[Special:Contributions/162.158.91.221|162.158.91.221]] 07:28, 17 August 2018 (UTC)<br />
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Should we add a column with examples of similar correct equations from the respective fields? Sebastian --[[Special:Contributions/172.68.110.4|172.68.110.4]] 09:33, 17 August 2018 (UTC)<br />
:That would definitely tidy up my attempts to provide context for Randall's versions. The challenge then is working in explanations for the correct equations as well as arguing over which examples should be used. [[User:Exxi|Exxi]] ([[User talk:Exxi|talk]]) 09:45, 17 August 2018 (UTC)<br />
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I don't think the part in parentheses about OH in the Chemistry equation explanation is correct. OH- would mean that it's negatively charged and has nothing to do with unpaired electrons of Oxygen. It would add another horror to the equation, though, as it wouldn't be charge preserving anymore. [[Special:Contributions/162.158.88.230|162.158.88.230]] 09:58, 17 August 2018 (UTC)<br />
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"Redshit". Best typo ever. Please keep it. [[Special:Contributions/172.69.54.177|172.69.54.177]] 10:13, 17 August 2018 (UTC)<br />
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;Deep physics equations<br />
The transcript is wrong here, the last letter is not a <math>\mu</math>, but a "u" with a cedilla: u̧. The math parser refuses to render it, though. [[Special:Contributions/162.158.88.230|162.158.88.230]] 05:54, 17 August 2018 (UTC)<br />
:Looks like it. But I don't think that letter exists even. --[[Special:Contributions/162.158.91.221|162.158.91.221]] 07:28, 17 August 2018 (UTC)<br />
:Is this equation a sort of nod to a Theory Of Everything which unifies quantum mechanics and gravity... H-hat (a Hamiltonian, which in quantum mechanics describes the total energy of a system, and usually runs in to problems describing large systems - such as the entire universe - where gravity or spacetime curvature effects matter) *minus* u0 (the relativistic mass of the whole system at time zero ie. the big bang) gives 0 (no energy everywhere always). Since mass is energy (e=mc^2) and mass is also the sole cause of gravity the two theories cleanly collapse together when mass is zero, and figuring out how to extend the theory to other less clean points on the mass axis is obviously a job for less profound physics? I've no ideas to explain the cedilla. [[Special:Contributions/141.101.98.28|141.101.98.28]] 08:49, 17 August 2018 (UTC)<br />
:It looks to me a little like a parody of the {{w|Wheeler-DeWitt_equation#Hamiltonian_constraint|Wheeler-DeWitt equation}} which (in theory) describes a wavefunction for the entire Universe. [[User:Exxi|Exxi]] ([[User talk:Exxi|talk]]) 09:06, 17 August 2018 (UTC)一<br />
: I'm just thrilled someone found the right character for it. I spent 20 minutes looking for the right u symbol without any luck at all. {{unsigned ip|172.68.143.132}}<br />
Is this poking fun at equation-filled blackboards in movies and cartoons? {{unsigned ip|172.68.254.42}}<br />
:Doesn't seem like it. These equations actually do look like the kinds of equations you would see in these fields. On blackboards in movies you tend to get equations that are pure nonsense. {{unsigned ip|172.68.143.132}}<br />
<br />
;Table layout at the explanation<br />
That oversized table is really bad layout. We've had this discussion many times before - tables should only be used for small contents. Right now I would run into too many edit conflicts but I'll change it to a proper floating text with small headers for each section. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 11:51, 17 August 2018 (UTC)<br />
:Done, looks much more like a real paper... --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 12:58, 17 August 2018 (UTC)<br />
<br />
;All number theory equation<br />
The explanation for math doesn't seem entirely correct. You can in fact extend the ring of integers (as well as rational and real numbers) with positive and negative infinity, but it won't be a ring anymore. Specifically, the infinities don't have an additive or multiplicative inverse (but 1/infinity = 0); and addition of positive and negative infinity, as well as the product of 0 and either infinity is undefined. However, these properties are not used in the above equation. What we ''can'' use is that <math>\forall n < \infty: n - \infty= -\infty </math>. We would thus have <math>K_n = \sum_{i=0}^{\infty}\sum_{\pi=0}^{\infty}(n-\pi)(i-e^{\pi-\infty}) = \sum_{i=0}^{\infty}\sum_{\pi=0}^{\infty}(n-\pi)(i-0) = \sum_{i=0}^{\infty}\sum_{\pi=0}^{\infty}(n-\pi)i= \sum_{i=0}^{\infty}i\sum_{\pi=n}^{\infty}-\pi= \sum_{i=0}^{\infty}i\cdot(-\infty)=-\infty</math>. Also, how often does one use e and pi in number theory? --[[User:Ycthiognass|Ycthiognass]] ([[User talk:Ycthiognass|talk]]) 12:11, 17 August 2018 (UTC)<br />
:Pi (or any other number) minus infinite is just absurd. You can use the infinite symbol only as a limit but NOT as number in calculations. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 12:33, 17 August 2018 (UTC)<br />
::It is not absurd. Adding the rules <math>n+\infty=\infty\text{ for }n>-\infty,n-\infty=-\infty\text{ for }n<\infty, \pm n\cdot\infty = \pm\infty\text{ for }n>0, \pm n\cdot(-\infty) = \mp\infty\text{ for }n>0,\frac1{\pm\infty}=0</math> gives you a consistent theory that is especially useful when talking about infinite sums and integrals. Would you say the term <math>n-\sum_{i=1}^\infty i</math> is absurd? --[[User:Ycthiognass|Ycthiognass]] ([[User talk:Ycthiognass|talk]]) 14:35, 17 August 2018 (UTC)<br />
<br />
;Chemistry equation<br />
OH should have a charge symbol: OH<sup>-</sup>. The actual reaction would be:<br />
<br />
CH<sub>4</sub> + OH<sup>-</sup> + heat -> CH<sub>3</sub><sup>-</sup> + H<sub>2</sub>O<br />
<br />
The methyl group can dissolve in water, and this is presumably happening in water, so this equation can work, just not the one provided by Randell. Reacting longer alkanes with bases is a way to make soaps, but the methyl group would be too reactive to be used this way. [[User:Nutster|Nutster]] ([[User talk:Nutster|talk]]) 13:13, 17 August 2018 (UTC)<br />
<br />
;Fluid Dynamics equation<br />
I believe the fraction 8/23 in the Fluid Dynamics equation is a Randallesque reference to the fractional approximation of pi = 22/7. It's probably not a coincidence that you get 8/23 from 22/7 if you invert it and add 1 to both the numerator and denominator. [[User:Ianrbibtitlht|Ianrbibtitlht]] ([[User talk:Ianrbibtitlht|talk]]) 15:19, 17 August 2018 (UTC)<br />
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;Gauge theory equation<br />
I think the transcript is missing a left superscript 0 before the turned xi. [[Special:Contributions/172.68.226.16|172.68.226.16]] 16:50, 17 August 2018 (UTC)</div>172.68.226.16https://www.explainxkcd.com/wiki/index.php?title=Talk:1866:_Russell%27s_Teapot&diff=143768Talk:1866: Russell's Teapot2017-08-07T18:43:10Z<p>172.68.226.16: 418</p>
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In this case, nesting the teapot in a catapult/cannon which is launched by another catapult/cannon might perhaps be sufficient to get past NASA regulations. (Catapults/cannons only launching the payload and not themselves...) <sub>--[[User:Nialpxe|<span style="color: #000; text-decoration: none;">Nialpxe</span>]], 2017. [[User_talk:Nialpxe|<span style="color: #000; text-decoration: none;">(Arguments welcome)</span>]]</sub><br />
:Though there's still the matter of an equal and opposite force pushing the satellite away from its gravitational bonds of the catapult. Even if the 2nd catapult is no longer associated with the Earth or Earth's gravity, the catapult will continue to be a launcher. That's just changing what it is launching *from*. [[Special:Contributions/172.68.58.125|172.68.58.125]] 18:31, 24 July 2017 (UTC)ColinHeico<br />
:But make sure it is a mobile cannon, otherwise it would not qualify as a launch '''vehicle'''. [[Special:Contributions/162.158.89.19|162.158.89.19]] 11:32, 21 July 2017 (UTC)<br />
::I immediately thought "railgun". And the payload can still be a rocket; once it's not touching the ground it's accelerating, not launching. (Also Russell failed to account for female barbers. Honestly, people!) [[Special:Contributions/108.162.241.4|108.162.241.4]] 09:42, 22 July 2017 (UTC)<br />
::: One such company did exist, Quicklaunch had the idea of launching via a space gun. https://en.m.wikipedia.org/wiki/Quicklaunch {{unsigned ip|172.68.141.142}}<br />
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::: He didn't need to account for female barbers (or anybody who isn't a man) because the barber in the paradox shaves precisely those men who don't shave themselves. He ''only'' shaves men, and all men in the town are ''only'' shaved by him or themselves. Everyone else is a completely different story, so they can be shaved by whoever they want (except the barber, who only shaves men). [[Special:Contributions/108.162.241.88|108.162.241.88]] 00:14, 23 July 2017 (UTC)<br />
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:::Only if you assume that females who are barbers don't shave their legs, armpits, or their various lady parts. This only further confuses the paradox. {{unsigned|Mjm87}}<br />
::::For much of Bertrand Russell's life, they didn't. http://mentalfloss.com/article/22511/when-did-women-start-shaving-their-pits [[Special:Contributions/108.162.241.4|108.162.241.4]] 09:42, 22 July 2017 (UTC)<br />
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:You wouldn't even need a cannon/catapult. If you put the satellite on a small rocket, and put that on a much larger rocket, you can have the big one launch itself, the smaller one, and the satellite. The regulation only says the satellite must be in a non-self-launching launch vehicle. It doesn't say it can't *also* be in a self-launching launch vehicle. -- [[Special:Contributions/108.162.246.113|108.162.246.113]] 20:06, 24 July 2017 (UTC)<br />
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When I first saw this comic I immediately thought of the Utah Teapot, it's a model used in computer graphics because it's simple and has both convex and concave surfaces. Both teapots, I would assume, (I've only just heard of Russel's Teapot so I could be wrong) are well known to different parts of the nerd community? {{unsigned ip|162.158.255.22}}<br />
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Hopefully it will support HTCPCP-TEA. [[Special:Contributions/108.162.241.34|108.162.241.34]] 17:48, 21 July 2017 (UTC)<br />
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i think people just really like teapot examples {{unsigned ip|108.162.246.23}}<br />
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:The major problem here is that CubeSats are currently only launched into Low Earth Orbit (LEO) and are expected to re-enter the atmosphere within days to weeks. Russell's teapot is (allegedly) in orbit between Earth and Mars and Cueball's device is not likely to have enough delta-v to leave Earth orbit. [[User:SteveBaker|SteveBaker]] ([[User talk:SteveBaker|talk]]) 18:18, 21 July 2017 (UTC)<br />
"A teapot orbits the Sun somewhere in space between the Earth and Mars" This implies that the teapot is physically located between Mars and Earth at all times. Which if true would be a highly irregular orbit requiring constant velocity changes, which is an impossible feat to achieve with current teapot technology. {{unsigned|Mjm87}}<br />
:Nonsense. It would be a ''highly regular orbit'' and many asteroids are already there, despite the most of them are between Mars and Jupiter (Asteroid-Belt):--[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 21:22, 21 July 2017 (UTC)<br />
::Since we're nitpicking. Having velocity changes does not preclude being in orbit: objects in orbit are always accelerating. Having a constant velocity change does preclude being in orbit, but it also precludes remaining between Earth and Mars, since it would result in eventually leaving the solar system.--[[Special:Contributions/172.68.54.112|172.68.54.112]] 19:45, 24 July 2017 (UTC)<br />
:::Still nonsense. The mean velocity of an (elliptic) orbit is constant, only the direction is changing. And there are many asteroids in stable orbits between Earth and Mars. Leaving the solar system would require many energy at those orbits, all human build probes (Pioneer, Voyager and New Horizons) had to use gravity assist at Jupiter to reach this target.--[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 14:12, 26 July 2017 (UTC)<br />
::::It sounds to me like you're missing the interpretation Mjm87 is trying to share. Yes, the way Russell meant it was that Russell's Teapot is between Mars and Earth in the same way that Earth is between Mars and the Sun, that this teapot is in a larger orbit than Earth and smaller than Mars. Mjm87's interpretation adds the idea that not only is it in such an orbit, but also in a direct line in between, always. In other words, that someone looking at Mars through a powerful telescope would always be able to see Russell's Teapot "in the way", like a little Mars eclipse. :) Staying in that spot would indeed take strange acceleration. I'm no astrophysicist or anything, but I imagine if I think of our galaxy as a clock face, with Earth always at the 12 o'clock position, that Mars would at some point be at 3 o'clock, at another time be at 9 o'clock, etc. (of course this is a 2D intepretation of a 3D situation, but I hope you get my point. Actually the third dimension would make this orbit even stranger) [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 05:16, 28 July 2017 (UTC)<br />
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I can see both of your points. As mjm87 says, "between the Earth and Mars", taken literally, would mean "on a line between the two planets", which would be a very unusual orbit. And, I agree, it would be impossible without constant velocity changes, so wouldn't be an "orbit" in the usual sense.<br />
On the other hand, I took Russell's words the way Dgbrt seems to have, as meaning "between the orbits of Earth and Mars", as this is the way most astronomers would interpret it. A don't know that there are "many" asteroids that remain between Earth and Mars, but there are quite a few crossing the space, and at least a few with average distances in that range. - N Kalanaga {{unsigned ip|162.158.74.159}}<br />
:There is also quantifier scope ambiguity there. I believe that there is a large constellation of teapot statites, and at any given moment at least one of them is directly between Earth and Mars. --[[Special:Contributions/172.68.54.58|172.68.54.58]] 06:29, 22 July 2017 (UTC)<br />
Since Russell was going for absurdity, I favour the more absurd interpretation namely Mjm87's. [[User:Capncanuck|Capncanuck]] ([[User talk:Capncanuck|talk]]) 08:21, 22 July 2017 (UTC)<br />
:Taking "on a line between the two planets" literally would simply reduce to "inside the orbit of Mars". The Earth moves faster than Mars and right now the Sun is exactly between them on that line. NASA, ESA, and ISRO can not communicate with their orbiters and rovers until the beginning of August (see {{w|Solar conjunction}}). So the meaning "between the orbits of Earth and Mars" is still much more plausible.--[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 16:11, 22 July 2017 (UTC)<br />
:What if it's in the Earth-Mars L1 point? Then it's always on a line between the two planets. [[User:Promethean|Promethean]] ([[User talk:Promethean|talk]]) 06:02, 26 July 2017 (UTC)<br />
::{{w|Lagrangian point}}s exist for Earth-Sun, Mars-Sun, or Moon-Earth (small object orbits a larger one). There is nothing similar for Earth-Mars. Earth moves faster around the sun and the closest approach happens every 26 months at a distance not less than 55 Mio. km. 13 months later the maximum distance is approx. 400 Mio. km and the sun is in the middle as it happens right now!--[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 13:46, 26 July 2017 (UTC)<br />
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Don't worry we have been working on it. Launching the project in a few months.<br />
https://www.instagram.com/p/BSmdiMSFBSb/?taken-by=hate_plow<br />
https://www.instagram.com/p/BSwW4MIlE0b/?taken-by=hate_plow<br />
[[User:Zackdougherty|Zackdougherty]] ([[User talk:Zackdougherty|talk]]) 03:10, 22 July 2017 (UTC)<br />
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:Actually, it couldn't be on a direct line between Earth and Mars because then it would be tremendously easier to find (or disprove)! If the teapot can be anywhere between the orbits, then that is a vastly larger space to look for a teapot and therefore more difficult to disprove. Similarly, it is unlikely there are a whole constellation because then it would be more likely to find at least one. [[Special:Contributions/172.68.34.94|172.68.34.94]] 03:19, 25 July 2017 (UTC)<br />
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Could some people (smarter than myself) make an attempt at labeling the items on the cube sat that Randall left at squiggles? Maybe starting from the top, clockwise? I'll start a table, but I'm sure someone will need to fix it. [[User:DanB|DanB]] ([[User talk:DanB|talk]]) 03:24, 25 July 2017 (UTC)<br />
:Personally, I suspect such a diagram wouldn't have the top labelled as "Teapot", but as "Payload". :) To me it looks even longer, so perhaps "Top Secret Specialty Payload" or something? [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 05:05, 1 August 2017 (UTC)<br />
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The title text refers to Russell's paradox, and it is funny that Russell came to it thinking about teaspoons : "The class of teaspoons, for example, is not another teaspoon, but the class of things that are not teaspoons, is one of the things that are not teaspoons." See https://math.stackexchange.com/questions/1046863/how-can-a-set-contain-itself for the exact source.<br />
[[Special:Contributions/198.41.242.47|198.41.242.47]] 08:29, 28 July 2017 (UTC)<br />
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Amusingly Russell's original words, atleast as far as I've seen them quoted, literally described the teapot as being a planet. They stated something like "what if I said that orbiting the sun between Earth and Mars was a small planet the shape and size of a teapot...". The "thought experiment" dies a pretty quick death when you consider the current IAU definition of a planet, that it must be large enough to pull itself into a sphere from self-gravity(no marks for the teapot) and it needs to be gravitatonally dominant in it's orbital regions (no chance for something so low in mass), although that latter point tends to provoke the Pluto debate. Either way , by the strict definition, there isn't a teapot shaped "planet".Also if you don't call the teapot a planet, but do stick to Russell's words about an elliptical orbit you can probably calculate that something so small waving about between the orbits of Earth and Mars will end up being ejected due to a gravitational tug or resonance somewhere, probably from Jupiter (given Jupiter's mass it perturbs just about anything even when things are inside the orbit of Mars), once again profound philosophy gets an unfortunate surprise from orbital dynamics.[[Special:Contributions/162.158.154.91|162.158.154.91]] 23:39, 2 August 2017 (UTC)<br />
:Nope. Russell said: "...a teapot orbits the Sun somewhere in space between the Earth and Mars." He didn't say the teapot is a planet. And in 1952 the {{w|IAU definition of planet|IAU definition from 2006}} didn't exist and Pluto was still a planet. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 18:55, 3 August 2017 (UTC)<br />
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How come that noone mentioned **418**? [[Special:Contributions/172.68.226.16|172.68.226.16]] 18:43, 7 August 2017 (UTC)</div>172.68.226.16