explain xkcd - User contributions [en]

3024: METAR

2024-12-13T19:18:51Z

162.158.154.235:

{{comic
| number = 3024
| date = December 13, 2024
| title = METAR
| image = metar_2x.png
| imagesize = 640x360px
| noexpand = true
| titletext = In the aviation world, they don't use AM/PM times. Instead, all times are assumed to be AM unless they're labeled NOTAM.
}}

==Explanation==
{{incomplete|Created by an Airbus3800 - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

{| class="wikitable"
|-
! Code !! Real Meaning !! According to the comic
|-
| METAR
|
|
|}

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

{{comic discussion}}

Talk:2053: Incoming Calls

2018-10-01T21:16:57Z

162.158.154.235:

The "other scammers" section is far too small. [[Special:Contributions/108.162.216.166|108.162.216.166]] 16:54, 1 October 2018 (UTC)

We have two title texts explanations. With slightly conflicting information. Combine and brush up or should we just do one or the other for now? I like the CBS source in the first so I think we should absolutely preserve that at least. [[User:Lukeskylicker|Lukeskylicker]] ([[User talk:Lukeskylicker|talk]]) 17:15, 1 October 2018 (UTC)

He forgot bill collectors. {{unsigned ip|162.158.63.52}}

As the link from the first title text explanation points out, they don't *need* your credit card or social security number as many phone companies, especially mobile companies, will allow a third party to add charges to your phone bill if you've agreed to pay the money. With that in mind, I don't think the second explanation flies. [[Special:Contributions/162.158.186.90|162.158.186.90]] 17:42, 1 October 2018 (UTC)

This only makes sense if it’s proportional or percentage based. But then that makes one wonder if some of this might be because the number of calls dropped over time. {{unsigned|Mr.Dude}}

There's a contradiction between "it's safe to assume that calls from his family didn't decrease over the years", and "Over time, Randall's friends and family have been less likely to make phone calls to him, likely due to the use of text messages and other messaging apps.". I'd suggest rephrasing the first part to say "it's possible the calls from family didn't decrease over the years, in which case they only make up a smaller fraction as the number of total calls increases since 1990.", or simply "some of the categories like family calls appear to be occurring less often but may only be decreasing in frequency in proportion to total calls" [[Special:Contributions/162.158.142.28|162.158.142.28]] 21:10, 1 October 2018 (UTC)

At least not being British he missed the PPI calls. [[Special:Contributions/162.158.154.235|162.158.154.235]] 21:16, 1 October 2018 (UTC)

2048: Curve-Fitting

2018-09-22T01:06:21Z

162.158.154.235: /* House of Cards */

{{comic
| number = 2048
| date = September 19, 2018
| title = Curve-Fitting
| image = curve_fitting.png
| titletext = Cauchy-Lorentz: "Something alarmingly mathematical is happening, and you should probably pause to Google my name and check what field I originally worked in."
}}

==Explanation==
{{incomplete|Please edit the explanation below and only mention here why it isn't complete. Do NOT delete this tag too soon.}}

An illustration of several plots of the same data with {{w|Curve fitting|curves fitted}} to the points, paired with conclusions that you might draw about the person who made them. This data, when plotted on an X/Y graph, looks somewhat random and there is a desire or need to determine some kind of pattern. With some kinds of data the pattern can be visually obvious, and perhaps a straight or diagonal line, represented by a simple mathematical formula, hits or comes very near hitting all the points. In other cases where it's not as intuitively obvious, one begins to look for more sophisticated mathematical formulas that appear to fit the data, in order to be able to extrapolate or interpolate other data that wasn't in the initial sampling.

When modeling such a problem statistically, it is common to search for trends, and fitted curves can help reveal these trends. Much of the work of a data scientist or statistician is knowing which fitting method to use for the data in question. Here we see various hypothetical scientists or statisticians each applying their own interpretations, and the comic mocks each of them for their various personal biases or other assorted excuses. In general, the researcher will specify the form of an equation for the line to be drawn, and an algorithm will produce the actual line.

Nonetheless scientists work much more seriously on the reliability of their assumptions by giving a value for the {{w|Standard deviation|standard deviation}} represented by the Greek letter sigma σ or the Latin letter s as a measure to quantify the amount of variation of the data points against the presented ''best fit''. If the σ-value isn't good enough an interpretation based on a specific fit wouldn't be accepted by the science community.

Since [[Randall]] gives no hint about the nature of the used data set - same in each graph - any fitting presented doesn't make any sense. The graphs could represent a star map, the votes for the latest elected presidents, or your recent invoices on power consumption. This comic just exaggerates various methods on interpreting data, but without the knowledge of the matter in the background nothing makes any sense.

===Linear===
[[File:Anscombe's quartet 3.svg|thumb|200px|Different data sets result in the same regression.]]
<math>f(x) = mx + b</math>

{{w|Linear regression}} is the most basic form of regression; it tries to find the straight line that best approximates the data. As it's the simplest, most widely taught form of regression, and in general derivable function are locally well approximated by a straight line, it's usually the first and most trivial attempt of fit.

The picture to the right shows how totally different data sets can result into the same line. It's obvious that some more basics about the nature of the data must be used to understand if this simple line really does make sense.

The comment below the graph ''"Hey, I did a regression."'' refers to the fact that this is just the easiest way of fitting data into a curve.

===Quadratic===
<math>f(x) = ax^2 + bx + c</math>

{{w|Polynomial regression|Quadratic fit}} (i.e. fitting a parabola through the data) is the lowest grade polynomial that can be used to fit data through a curved line; if the data exhibits clearly "curved" behavior (or if the experimenter feels that its growth should be more than linear), a parabola is often the first, easiest, stab at fitting the data.

The comment below the graph ''"I wanted a curved line, so I made one with math."'' refers to the fact that quadratic correlations like this are mathematically valid (and probably the simplest kind of curve in math) but rarely occur in real life.

===Logarithmic===
[[File:Logarithm_plots.png|thumb|200px|Common logarithm functions.]]
<math>f(x) = a\log_b(x) + c</math>

A {{w|Logarithm|logarithmic}} curve growths slower on higher values, but still grows without bound to infinity rather than approaching a horizontal {{w|asymptote}}. The small ''b'' in the formula represents the base which is in most cases 2, ''{{w|e (mathematical constant)|e}}'', or 10. If the data presumably does approach a horizontal asymptote then this fit isn't an effective method to explain the nature of the data.

The comment below the graph ''"Look, it's tapering off!"'' builds up the impression that the data diminishes while under this fit it's still growing to infinity, only much slower than a linear regression does.

===Exponential===
[[File:Exponential.svg|thumb|200px|Exponential growth (green) compared to other functions.]]
<math>f(x) = a\cdot b^x + c</math>

An {{w|Exponential growth|exponential curve}}, on the contrary, is typical of a phenomenon whose growth gets rapidly faster and faster - a common case is a process that generates stuff that contributes to the process itself, think bacteria growth or compound interest.

The logarithmic and exponential interpretations could very easily be fudged or engineered by a researcher with an agenda (such as by taking a misleading subset or even outright lying about the regression), which the comic mocks by juxtaposing them side-by-side on the same set of data.

The comment below the graph ''"Look, it's growing uncontrollably!"'' gives an other frivolous statement suggesting something like chaos. Also this even faster growth is well defined and has no asymptote at both axes.

===LOESS===
A {{w|Local regression|LOESS fit}} doesn't use a single formula to fit all the data, but approximates data points locally using different polynomials for each "zone" (weighting differently data points as they get further from it) and patching them together. As it has much more degrees of freedom compared to a single polynomial, it generally "fits better" to any data set, although it is generally impossible to derive any strong, "clean" mathematical correlation from it - it is just a nice smooth line that approximates well the data points, with a good degree of rejection from outliers.

The comment below the graph ''"I'm sophisticated, not like those bumbling polynomial people."'' emphasis this more complicated interpretation but without a simple mathematical description it's not much helpful to find academic descriptions on the underlying matter.

===Linear, No Slope===
<math>f(x) = c</math>

Apparently, the person making this line figured out pretty early on that their data analysis was turning into a scatter plot, and wanted to escape their personal stigma of scatter plots by drawing an obviously false regression line on top of it. Alternatively, they were hoping the data would be flat, and are trying to pretend that there's no real trend to the data by drawing a horizontal trend line.

The comment below the graph ''"I'm making a scatter plot but I don't want to."'' is probably done by a student who isn't happy with it's choice of field of study.

===Logistic===
[[File:Logistic-curve.svg|thumb|200px|A standard logistic function between the values ''0'' and ''1''.]]
The {{w|Logistic regression|logistic regression}} is taken when a variable can take binary results such as "0" and "1" or "old" and "young".

The curve provides a smooth, S-shaped transition curve between two flat intervals (like "0" and "1").

The comment below the graph ''"I need to connect these two lines, but my first idea didn't have enough math."'' implies the experimenter just wants to find a mathematically-respectable way to link two flat lines.

===Confidence Interval===
Not a type of curve fitting, but a method of depicting the predictive power of a curve.

Providing a confidence interval over the graph shows the uncertainty of the acquired data, thus acknowledging the uncertain results of the experiment, and showing the will not to "cheat" with "easy" regression curves.

The comment below the graph ''"Listen, science is hard. But I'm a serious person doing my best."'' is just an honest statement about this uncertainty.

===Piecewise===
Mapping different curves to different segments of the data. This is a legitimate strategy, but the different segments should be meaningful, such as if they were pulled from different populations.

This kind of fit would arise naturally in a study based on a regression discontinuity design. For instance, if students who score below a certain cutoff must take remedial classes, the line for outcomes of those below the cutoff would reasonably be separate from the one for outcomes above the cutoff; the distance between the end of the two lines could be considered the effect of the treatment, under certain assumptions. This kind of study design is used to investigate causal theories, where mere correlation in observational data is not enough to prove anything. Thus, the associated text would be appropriate; there is a theory, and data that might prove the theory is hard to find.

One notable time this is used is when a researcher studying housing economics is trying to identify housing submarkets. The assumption is that if two proposed markets are truly different, they will be better described using two different regression functions than if one were to be used.

The additional curved lines visible in the graph are the kind of confidence intervals you'd get from a simple OLS regression if the standard assumptions were valid. In the case of two separate regressions, it would be surprising if all those assumptions (that is, i.i.d. Normal residuals around an underlying perfectly-linear function) were in fact valid for each part, especially if the slopes are not equal.

A classical example in physics are the different theories to explain the black body radiation at the end of the 19th century. The {{w|Wien approximation}} was good for small wavelengths while the {{w|Rayleigh–Jeans law}} worked for the larger scales (large wavelength means low frequency and thus low energy.) But there was a gap in the middle which was filled by the {{w|Planck's law}} in 1900.

The comment below the graph ''"I have a theory, and this is the only data I could find."'' is a bit ambiguous because there are many data points ignored. Without an explanation why only a subset of the data is used this isn't a useful interpretation at all.

===Connecting lines===
This is often used to smooth gaps in measurements. A simple example is the weather temperature which is often measured in distinct intervals. When the intervals are high enough it's safe to assume that the temperature didn't change that much between them and connecting the data points by lines doesn't distort the real situation in many cases.

The comment below the graph ''"I clicked 'Smooth Lines' in {{w|Microsoft Excel|Excel}}."'' refers to the well known spreadsheet application from {{w|Microsoft Office}}. Like other spreadsheet applications it has the feature to visualize data from a table into a graph by many ways. "Smooth Lines" is a setting meant for use on a {{w|line graph}} and is purely aesthetic; as it simply joins up every point rather than finding a sensible line, it is not suitable for regression.

===Ad-Hoc Filter===
Drawing a bunch of different lines by hand, keeping in only the data points perceived as "good". Not really useful except for marketing purposes.

The comment below the graph ''"I had an idea for how to clean up the data. What do you think?"'' admits that in fact the data is whitewashed and tightly focused to a result the presenter wants to show.

===House of Cards===
Not a real method, but a common consequence of misapplication of statistical methods: a curve can be generated that fits the data extremely well, but immediately becomes absurd as soon as one glances outside the training data sample range, and your analysis comes crashing down "like a house of cards". This is a type of ''overfitting''. In other words, the model may do quite well for (approximately) {{w|Interpolation|interpolating}} between values in the sample range, but not extend at all well to {{w|Extrapolation|extrapolating}} values outside that range.

''Note:'' Exact polynomial fitting, a fit which gives the unique <math>(n-1)</math>th degree polynomial through <math>n</math> points, often display this kind of behaviour.

The comment below the graph ''"As you can see, this model smoothly fits the- wait no no don't extend it AAAAAA!!"'' refers to a curve which fits the data points relatively well within the graph's boundaries, but beyond those bounds fails to match at all.

The name is also a reference to the TV show ''{{w|House of Cards (U.S. TV series)|House of Cards}}'' ("WAIT NO, NO, DON'T EXTEND IT!").

===Cauchy-Lorentz (title text)===
{{w|Cauchy_distribution|Cauchy-Lorentz}} is a continuous probability distribution which does not have an expected value or a defined variance. This means that the law of large numbers does not hold and that estimating e.g. the sample mean will diverge (be all over the place) the more data points you have. Hence very troublesome (mathematically alarming).

Since so many different models can fit this data set at first glance, Randall may be making a point about how if a data set is sufficiently messy, you can read any trend you want into it, and the trend that is chosen may say more about the researcher than about the data. This is a similar sentiment to [[1725: Linear Regression]], which also pokes fun at dubious trend lines on scatterplots.

A brief Google search reveals that Augustin-Louis Cauchy originally worked as a junior engineer in a managerial position. Upon his acceptance to the Académie des Sciences in March 1816, many of his peers expressed outrage. Despite his early work in "mere" engineering, Cauchy is widely regarded as one of the founding influences in the rigorous study of calculus & accompanying proofs.

Alternately, the title-text could be implying that the person who applied the Cauchy-Lorentz curve-fitting method may not be well qualified to the task assigned.

==Transcript==
:'''Curve-Fitting Methods'''
:and the messages they send

:[In a single frame twelve scatter plots with unlabeled x- and y-axes are shown. Each plot consists of the same data-set of approximately thirty points located all over the plot but slightly more distributed around the diagonal. Every plot shows in red a different fitting method which is labeled on top in gray.]

:[The first plot shows a line starting at the left bottom above the x-axis rising towards the points to the right.]
:Linear
:"Hey, I did a regression."

:[The second plot shows a curve falling slightly down and then rising up to the right.]
:Quadratic
:"I wanted a curved line, so I made one with math."

:[At the third plot the curve starts near the left bottom and increases more and more less to the right.]
:Logarithmic
:"Look, it's tapering off!"

:[The fourth plot shows a curve starting near the left bottom and increases more and more steeper towards the right.]
:Exponential
:"Look, it's growing uncontrollably!"

:[The fifth plot uses a fitting to match many points. It starts at the left bottom, increases, then decreases, then rapidly increasing again, and finally reaching a plateau.]
:LOESS
:"I'm sophisticated, not like those bumbling polynomial people."

:[The sixth plot simply shows a line above but parallel to the x-axis.]
:Linear, no slope
:"I'm making a scatter plot but I don't want to."

:[At plot #7 starts at a plateau above the x-axis, then increases, and finally reaches a higher plateau.]
:Logistic
:"I need to connect these two lines, but my first idea didn't have enough Math."

:[Plot #8 shows two red lines embedding most points and the area between is painted as a red shadow.]
:Confidence interval
:"Listen, science is hard. But I'm a serious person doing my best."

:[Plot #9 shows two not connected lines, one at the lower left half, and one higher at the right. Both have smaller curved lines in light red above and below.]
:Piecewise
:"I have a theory, and this is the only data I could find."

:[The plot at the left bottom shows a line connecting all points from left to right, resulting in a curve going many times up and down.]
:Connecting lines
:"I clicked 'Smooth Lines' in Excel."

:[The next to last plot shows a echelon form, connecting a few real and some imaginary points.]
:Ad-Hoc filter
:"I had an idea for how to clean up the data. What do you think?"

:[The last plot shows a wave with increasing peak values. Finally the plot of the wave is continued beyond the x- and y-axis borders.]
:House of Cards
:"As you can see, this model smoothly fits the- ''wait no no don't extend it AAAAAA!!''"

==Trivia==
*This is the comic 2048, or 211. In addition to being the name of a popular app referenced in [[1344: Digits]], this is an extremely round number in binary (100,000,000,0002). [[1000: 1000 Comics]] pointed out that comic 1024 would be a round number, but there were not any comics noting 2048.

*This comic is similar to [[977: Map Projections]] which also uses a scientific method not commonly thought about by the general public to determine specific characteristics of one's personality and approach to science.

*Regressions have been the subject of several previous comics. [[1725: Linear Regression]] was about linear regressions on uncorrelated or poorly correlated data. [[1007: Sustainable]] and [[1204: Detail]] depict linear regressions on data that was actually logistic, leading to bizarre extrapolations. [[605: Extrapolating]] shows a line extrapolating from just two data points.

{{comic discussion}}

[[Category:Comics with color]]
[[Category:Scatter plots]]
[[Category:Math]]
[[Category:Science]]

2048: Curve-Fitting

2018-09-22T00:39:11Z

162.158.154.235: /* Quadratic */ comment didn't make sense - linear reg isn't a *curved* line

{{comic
| number = 2048
| date = September 19, 2018
| title = Curve-Fitting
| image = curve_fitting.png
| titletext = Cauchy-Lorentz: "Something alarmingly mathematical is happening, and you should probably pause to Google my name and check what field I originally worked in."
}}

==Explanation==
{{incomplete|Please edit the explanation below and only mention here why it isn't complete. Do NOT delete this tag too soon.}}

An illustration of several plots of the same data with {{w|Curve fitting|curves fitted}} to the points, paired with conclusions that you might draw about the person who made them. This data, when plotted on an X/Y graph, looks somewhat random and there is a desire or need to determine some kind of pattern. With some kinds of data the pattern can be visually obvious, and perhaps a straight or diagonal line, represented by a simple mathematical formula, hits or comes very near hitting all the points. In other cases where it's not as intuitively obvious, one begins to look for more sophisticated mathematical formulas that appear to fit the data, in order to be able to extrapolate or interpolate other data that wasn't in the initial sampling.

When modeling such a problem statistically, it is common to search for trends, and fitted curves can help reveal these trends. Much of the work of a data scientist or statistician is knowing which fitting method to use for the data in question. Here we see various hypothetical scientists or statisticians each applying their own interpretations, and the comic mocks each of them for their various personal biases or other assorted excuses. In general, the researcher will specify the form of an equation for the line to be drawn, and an algorithm will produce the actual line.

Nonetheless scientists work much more seriously on the reliability of their assumptions by giving a value for the {{w|Standard deviation|standard deviation}} represented by the Greek letter sigma σ or the Latin letter s as a measure to quantify the amount of variation of the data points against the presented ''best fit''. If the σ-value isn't good enough an interpretation based on a specific fit wouldn't be accepted by the science community.

Since [[Randall]] gives no hint about the nature of the used data set - same in each graph - any fitting presented doesn't make any sense. The graphs could represent a star map, the votes for the latest elected presidents, or your recent invoices on power consumption. This comic just exaggerates various methods on interpreting data, but without the knowledge of the matter in the background nothing makes any sense.

===Linear===
[[File:Anscombe's quartet 3.svg|thumb|200px|Different data sets result in the same regression.]]
<math>f(x) = mx + b</math>

{{w|Linear regression}} is the most basic form of regression; it tries to find the straight line that best approximates the data. As it's the simplest, most widely taught form of regression, and in general derivable function are locally well approximated by a straight line, it's usually the first and most trivial attempt of fit.

The picture to the right shows how totally different data sets can result into the same line. It's obvious that some more basics about the nature of the data must be used to understand if this simple line really does make sense.

The comment below the graph ''"Hey, I did a regression."'' refers to the fact that this is just the easiest way of fitting data into a curve.

===Quadratic===
<math>f(x) = ax^2 + bx + c</math>

{{w|Polynomial regression|Quadratic fit}} (i.e. fitting a parabola through the data) is the lowest grade polynomial that can be used to fit data through a curved line; if the data exhibits clearly "curved" behavior (or if the experimenter feels that its growth should be more than linear), a parabola is often the first, easiest, stab at fitting the data.

===Logarithmic===
[[File:Logarithm_plots.png|thumb|200px|Common logarithm functions.]]
<math>f(x) = a\log_b(x) + c</math>

A {{w|Logarithm|logarithmic}} curve growths slower on higher values, but still grows without bound to infinity rather than approaching a horizontal asymptote. The small ''b'' in the formula represents the base which is in most cases 2, ''{{w|e (mathematical constant)|e}}'', or 10. If the data presumably does approach a horizontal asymptote then this fit isn't an effective method to explain the nature of the data.

The comment below the graph ''"Look, it's tapering off!"'' builds up the impression that the data diminishes while under this fit it's still growing to infinity, only much slower than a linear regression does.

===Exponential===
[[File:Exponential.svg|thumb|200px|Exponential growth (green) compared to other functions.]]
<math>f(x) = a\cdot b^x + c</math>

An {{w|Exponential growth|exponential curve}}, on the contrary, is typical of a phenomenon whose growth gets rapidly faster and faster - a common case is a process that generates stuff that contributes to the process itself, think bacteria growth or compound interest.

The logarithmic and exponential interpretations could very easily be fudged or engineered by a researcher with an agenda (such as by taking a misleading subset or even outright lying about the regression), which the comic mocks by juxtaposing them side-by-side on the same set of data.

The comment below the graph ''"Look, it's growing uncontrollably!"'' gives an other frivolous statement suggesting something like chaos. Also this even faster growth is well defined and has no asymptote at both axes.

===LOESS===
A {{w|Local regression|LOESS fit}} doesn't use a single formula to fit all the data, but approximates data points locally using different polynomials for each "zone" (weighting differently data points as they get further from it) and patching them together. As it has much more degrees of freedom compared to a single polynomial, it generally "fits better" to any data set, although it is generally impossible to derive any strong, "clean" mathematical correlation from it - it is just a nice smooth line that approximates well the data points, with a good degree of rejection from outliers.

The comment below the graph ''"I'm sophisticated, not like those bumbling polynomial people."'' emphasis this more complicated interpretation but without a simple mathematical description it's not much helpful to find academic descriptions on the underlying matter.

===Linear, No Slope===
<math>f(x) = c</math>

Apparently, the person making this line figured out pretty early on that their data analysis was turning into a scatter plot, and wanted to escape their personal stigma of scatter plots by drawing an obviously false regression line on top of it. Alternatively, they were hoping the data would be flat, and are trying to pretend that there's no real trend to the data by drawing a horizontal trend line.

The comment below the graph ''"I'm making a scatter plot but I don't want to."'' is probably done by a student who isn't happy with it's choice of field of study.

===Logistic===
[[File:Logistic-curve.svg|thumb|200px|A standard logistic function between the values ''0'' and ''1''.]]
The {{w|Logistic regression|logistic regression}} is taken when a variable can take binary results such as "0" and "1" or "old" and "young".

The curve provides a smooth, S-shaped transition curve between two flat intervals (like "0" and "1").

The comment below the graph ''"I need to connect these two lines, but my first idea didn't have enough Math."'' implys the experimenter just wants to find a mathematically-respectable way to link two flat lines.

===Confidence Interval===
Not a type of curve fitting, but a method of depicting the predictive power of a curve.

Providing a confidence interval over the graph shows the uncertainty of the acquired data, thus acknowledging the uncertain results of the experiment, and showing the will not to "cheat" with "easy" regression curves.

The comment below the graph ''"Listen, science is hard. But I'm a serious person doing my best."'' is just an honest statement about this uncertainty.

===Piecewise===
Mapping different curves to different segments of the data. This is a legitimate strategy, but the different segments should be meaningful, such as if they were pulled from different populations.

This kind of fit would arise naturally in a study based on a regression discontinuity design. For instance, if students who score below a certain cutoff must take remedial classes, the line for outcomes of those below the cutoff would reasonably be separate from the one for outcomes above the cutoff; the distance between the end of the two lines could be considered the effect of the treatment, under certain assumptions. This kind of study design is used to investigate causal theories, where mere correlation in observational data is not enough to prove anything. Thus, the associated text would be appropriate; there is a theory, and data that might prove the theory is hard to find.

One notable time this is used is when a researcher studying housing economics is trying to identify housing submarkets. The assumption is that if two proposed markets are truly different, they will be better described using two different regression functions than if one were to be used.

The additional curved lines visible in the graph are the kind of confidence intervals you'd get from a simple OLS regression if the standard assumptions were valid. In the case of two separate regressions, it would be surprising if all those assumptions (that is, i.i.d. Normal residuals around an underlying perfectly-linear function) were in fact valid for each part, especially if the slopes are not equal.

A classical example in physics are the different theories to explain the black body radiation at the end of the 19th century. The {{w|Wien approximation}} was good for small wavelengths while the {{w|Rayleigh–Jeans law}} worked for the larger scales (large wavelength means low frequency and thus low energy.) But there was a gap in the middle which was filled by the {{w|Planck's law}} in 1900.

The comment below the graph ''"I have a theory, and this is the only data I could find."'' is a bit ambiguous because there are many data points ignored. Without an explanation why only a subset of the data is used this isn't a useful interpretation at all.

===Connecting lines===
This is often used to smooth gaps in measurements. A simple example is the weather temperature which is often measured in distinct intervals. When the intervals are high enough it's safe to assume that the temperature didn't change that much between them and connecting the data points by lines doesn't distort the real situation in many cases.

The comment below the graph ''"I clicked 'Smooth Lines' in Excel."'' refers to the well known spreadsheet application from Microsoft. Like other spreadsheet applications it has the feature to visualize data from a table into a graph by many ways. The usage of the ''Smooth Lines'' feature here just sounds more like playing rather than investigating.

===Ad-Hoc Filter===
Drawing a bunch of different lines by hand, keeping in only the data points perceived as "good". Not really useful except for marketing purposes.

The comment below the graph ''"I had an idea for how to clean up the data. What do you think?"'' admits that in fact the data is whitewashed and tightly focused to a result the presenter wants to show.

===House of Cards===
Not a real method, but a common consequence of mis-application of statistical methods: a curve can be generated that fits the data extremely well, but immediately becomes absurd as soon as one glances outside the training data sample range, and your analysis comes crashing down "like a house of cards". This is a type of ''overfitting''. In other words, the model may do quite well for (approximately) {{w|Interpolation|interpolating}} between values in the sample range, but not extend at all well to {{w|Extrapolation|extrapolating}} values outside that range.

''Note:'' Exact polynomial fitting, a fit which gives the unique (n-1)-th degree polynomial through n points, often display this kind of behaviour.

The comment below the graph ''"As you can see, this model smoothly fits the- wait no no don't extend it AAAAAA!!"'' refers to a curve which fits the data points relatively well within the graph's boundaries, but beyond those bounds fails to match at all.

Also a potential reference to the TV show, House of Cards ("WAIT NO, NO, DON'T EXTEND IT!").

===Cauchy-Lorentz (title text)===
{{w|Cauchy_distribution|Cauchy-Lorentz}} is a continuous probability distribution which does not have an expected value or a defined variance. This means that the law of large numbers does not hold and that estimating e.g. the sample mean will diverge (be all over the place) the more data points you have. Hence very troublesome (mathematically alarming).

Since so many different models can fit this data set at first glance, Randall may be making a point about how if a data set is sufficiently messy, you can read any trend you want into it, and the trend that is chosen may say more about the researcher than about the data. This is a similar sentiment to [[1725: Linear Regression]], which also pokes fun at dubious trend lines on scatterplots.

A brief Google search reveals that Augustin-Louis Cauchy originally worked as a junior engineer in a managerial position. Upon his acceptance to the Académie des Sciences in March 1816, many of his peers expressed outrage. Despite his early work in "mere" engineering, Cauchy is widely regarded as one of the founding influences in the rigorous study of calculus & accompanying proofs.

==Transcript==
:'''Curve-Fitting Methods'''
:and the messages they send

:[In a single frame twelve scatter plots with unlabeled x- and y-axes are shown. Each plot consists of the same data-set of approximately thirty points located all over the plot but slightly more distributed around the diagonal. Every plot shows in red a different fitting method which is labeled on top in gray.]

:[The first plot shows a line starting at the left bottom above the x-axis rising towards the points to the right.]
:Linear
:"Hey, I did a regression."

:[The second plot shows a curve falling slightly down and then rising up to the right.]
:Quadratic
:"I wanted a curved line, so I made one with Math."

:[At the third plot the curve starts near the left bottom and increases more and more less to the right.]
:Logarithmic
:"Look, it's tapering off!"

:[The fourth plot shows a curve starting near the left bottom and increases more and more steeper towards the right.]
:Exponential
:"Look, it's growing uncontrollably!"

:[The fifth plot uses a fitting to match many points. It starts at the left bottom, increases, then decreases, then rapidly increasing again, and finally reaching a plateau.]
:LOESS
:"I'm sophisticated, not like those bumbling polynomial people."

:[The sixth plot simply shows a line above but parallel to the x-axis.]
:Linear, no slope
:"I'm making a scatter plot but I don't want to."

:[At plot #7 starts at a plateau above the x-axis, then increases, and finally reaches a higher plateau.]
:Logistic
:"I need to connect these two lines, but my first idea didn't have enough Math."

:[Plot #8 shows two red lines embedding most points and the area between is painted as a red shadow.]
:Confidence interval
:"Listen, science is hard. But I'm a serious person doing my best."

:[Plot #9 shows two not connected lines, one at the lower left half, and one higher at the right. Both have smaller curved lines in light red above and below.]
:Piecewise
:"I have a theory, and this is the only data I could find."

:[The plot at the left bottom shows a line connecting all points from left to right, resulting in a curve going many times up and down.]
:Connecting lines
:"I clicked 'Smooth Lines' in Excel."

:[The next to last plot shows a echelon form, connecting a few real and some imaginary points.]
:Ad-Hoc filter
:"I had an idea for how to clean up the data. What do you think?"

:[The last plot shows a wave with increasing peak values. Finally the plot of the wave is continued beyond the x- and y-axis borders.]
:House of Cards
:"As you can see, this model smoothly fits the- ''wait no no don't extend it AAAAAA!!''"

==Trivia==
*This is the comic 2048, or 211. In addition to being the name of a popular app referenced in [[1344: Digits]], this is an extremely round number in binary (100,000,000,0002). [[1000: 1000 Comics]] pointed out that comic 1024 would be a round number, but there were not any comics noting 2048.

*This comic is similar to [[977: Map Projections]] which also uses a scientific method not commonly thought about by the general public to determine specific characteristics of one's personality and approach to science.

*Regressions have been the subject of several previous comics. [[1725: Linear Regression]] was about linear regressions on uncorrelated or poorly correlated data. [[1007: Sustainable]] and [[1204: Detail]] depict linear regressions on data that was actually logistic, leading to bizarre extrapolations. [[605: Extrapolating]] shows a line extrapolating from just two data points.

{{comic discussion}}

[[Category:Comics with color]]
[[Category:Scatter plots]]
[[Category:Math]]
[[Category:Science]]

2045: Social Media Announcement

2018-09-13T06:47:07Z

162.158.154.235: Grammar

{{comic
| number = 2045
| date = September 12, 2018
| title = Social Media Announcement
| image = social_media_announcement.png
| titletext = Why I'm Moving Most of My Social Activity to Slack, Then Creating a Second Slack to Avoid the People in the First One, Then Giving Up on Social Interaction Completely, Then Going Back to Texting
}}

==Explanation==
{{incomplete|Too much focus on mastodon, not enough on the overall concept of the comic Do NOT delete this tag too soon.}}

In 2018, especially after {{w|Facebook}} privacy abuses were revealed in the {{w|Cambridge_Analytica#Privacy_issues|Cambridge Analytica scandal}}, many individuals began seeking alternatives. The #deletefacebook hashtag peaked around April 2018, and in some communities, this type of "why I'm leaving Facebook" announcements were popular.

{{w|Mastodon (software)|Mastodon}} is a distributed, federated social network with microblogging features similar to {{w|Twitter}}. "Federated" means that there is one app hosted in many places, so users can choose a host that meets their needs, but everyone can still talk to each other, similar to email. Near the peak of #deletefacebook, mastodon became trending as a [https://motherboard.vice.com/en_us/article/783akg/mastodon-is-like-twitter-without-nazis-so-why-are-we-not-using-it twitter alternative with less nazis].

The word {{w|Mastodon}} specifies a Mammut.

{{w|Wil Wheaton}} famously moved to Mastodon from Twitter, [https://news.avclub.com/wil-wheaton-on-quitting-social-media-i-don-t-deserve-1828743467 but was ultimately disappointed by the experience], because while Mastodon's community is generally less toxic, it does not yet have the tools to handle the kind of targeted harassment that a celebrity might face.

{{w|Microsoft}} has been buying up professional-themed social media platforms lately, such as {{w|LinkedIn}}, intending to integrate them more fluidly with their enterprise software suite. Mastodon seems an unlikely target for an acquisition, since its decentralized nature means that one corporate entity can't control it, and the culture there is decidedly unprofessional as of this comic.

The title text presents an alternative approach by moving most social activities to the cloud-based proprietary team collaboration platform {{w|Slack (software)|Slack}}. After making his first workspace in Slack he suggests that he wishes to avoid the people invited, so he creates a second account and a new workspace. This also didn't last long and he stops interacting on social media entirely. As a result he just writes texts and is probably not showing them to anyone.

==Trivia==
In the original version of this comic, Cueball misspelled "Mastodon" as "Mastadon".

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

:[Cueball sitting in front of a laptop typing.]
:Why I'm Quitting Facebook, Joining LinkedIn, Deleting My LinkedIn, Rejoining Facebook, Quitting Twitter, Getting Locked Out of Facebook, Moving to Mastadon, and Lobbying Microsoft to Take Over Mastadon and Merge It With LinkedIn: A Manifesto.

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Social networking]]

2045: Social Media Announcement

2018-09-13T06:46:14Z

162.158.154.235: Someone misread the title text, he makes a new account to avoid the people not the old messages

{{comic
| number = 2045
| date = September 12, 2018
| title = Social Media Announcement
| image = social_media_announcement.png
| titletext = Why I'm Moving Most of My Social Activity to Slack, Then Creating a Second Slack to Avoid the People in the First One, Then Giving Up on Social Interaction Completely, Then Going Back to Texting
}}

==Explanation==
{{incomplete|Too much focus on mastodon, not enough on the overall concept of the comic Do NOT delete this tag too soon.}}

In 2018, especially after {{w|Facebook}} privacy abuses were revealed in the {{w|Cambridge_Analytica#Privacy_issues|Cambridge Analytica scandal}}, many individuals began seeking alternatives. The #deletefacebook hashtag peaked around April 2018, and in some communities, this type of "why I'm leaving Facebook" announcements were popular.

{{w|Mastodon (software)|Mastodon}} is a distributed, federated social network with microblogging features similar to {{w|Twitter}}. "Federated" means that there is one app hosted in many places, so users can choose a host that meets their needs, but everyone can still talk to each other, similar to email. Near the peak of #deletefacebook, mastodon became trending as a [https://motherboard.vice.com/en_us/article/783akg/mastodon-is-like-twitter-without-nazis-so-why-are-we-not-using-it twitter alternative with less nazis].

The word {{w|Mastodon}} specifies a Mammut.

{{w|Wil Wheaton}} famously moved to Mastodon from Twitter, [https://news.avclub.com/wil-wheaton-on-quitting-social-media-i-don-t-deserve-1828743467 but was ultimately disappointed by the experience], because while Mastodon's community is generally less toxic, it does not yet have the tools to handle the kind of targeted harassment that a celebrity might face.

{{w|Microsoft}} has been buying up professional-themed social media platforms lately, such as {{w|LinkedIn}}, intending to integrate them more fluidly with their enterprise software suite. Mastodon seems an unlikely target for an acquisition, since its decentralized nature means that one corporate entity can't control it, and the culture there is decidedly unprofessional as of this comic.

The title text presents an alternative approach by moving most social activities to the cloud-based proprietary team collaboration platform {{w|Slack (software)|Slack}}. After making his first workspace in Slack he suggests that he not wishes to avoid the people invited, so he creates a second account and a new workspace. This also didn't last long and he stops interacting on social media entirely. As a result he just writes texts and is probably not showing them to anyone.

==Trivia==
In the original version of this comic, Cueball misspelled "Mastodon" as "Mastadon".

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

:[Cueball sitting in front of a laptop typing.]
:Why I'm Quitting Facebook, Joining LinkedIn, Deleting My LinkedIn, Rejoining Facebook, Quitting Twitter, Getting Locked Out of Facebook, Moving to Mastadon, and Lobbying Microsoft to Take Over Mastadon and Merge It With LinkedIn: A Manifesto.

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Social networking]]

Talk:2042: Rolle's Theorem

2018-09-07T07:16:00Z

162.158.154.235:

Now we wait for https://en.wikipedia.org/wiki/Munroes_theorem. [[Special:Contributions/172.69.54.165|172.69.54.165]] 15:51, 5 September 2018 (UTC)
:Can't wait to see how long it takes to remove the article. [[User:Linker|Linker]] ([[User talk:Linker|talk]]) 17:05, 5 September 2018 (UTC)

:Proposed ideas for Munroe's Law:
::- Any seemingly simple idea will be difficult to prove; the simpler it seems, the harder the proof.
::- Any proof which is discovered by a layperson will have been previously discovered by an expert (or an "expert") in the field.
:[[User:Rajakiit|Raj-a-Kiit]] ([[User talk:Rajakiit|talk]]) 17:57, 5 September 2018 (UTC)
:I do not have the time to do it good, so here a suggestion: Would someone go to the wikipedia page of Rolle's theorem and add a "in popular culture" section? may be a first? Not even "Nash equilibrum" has that :-) [[Special:Contributions/162.158.234.16|162.158.234.16]] 08:13, 6 September 2018 (UTC)

I feel like Euclid beat Randall to the punch here, a couple millennia. [[Special:Contributions/162.158.155.146|162.158.155.146]] 16:54, 5 September 2018 (UTC)

I don't see that Thales has proven Randall's theorem. Do not to be confused with {{w|Thales's theorem}}, that's about right angles. Maybe I'm blind or just dumb, but if so it has to be explained with more traceable background. I just believe that this diagonal is so trivial that even the ancient Greeks weren't engaged on a proof. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 21:38, 5 September 2018 (UTC)
* From {{w|Thales|Wikipedia}}: Other quotes from Proclus list more of Thales' mathematical achievements: "They say that Thales was the first to demonstrate that the circle is bisected by the diameter, the cause of the bisection being the unimpeded passage of the straight line through the centre." [[User:Alexei Kopylov|Alexei Kopylov]] ([[User talk:Alexei Kopylov|talk]]) 05:39, 6 September 2018 (UTC)
* On the other hand not all historian believe Proclus. But van der Waerden does: [https://books.google.com/books?id=HK3vCAAAQBAJ&pg=PA88#v=onepage&q&f=false]. [[User:Alexei Kopylov|Alexei Kopylov]] ([[User talk:Alexei Kopylov|talk]]) 05:49, 6 September 2018 (UTC)

:''Rolle's Theorem counterexample?''
Isn't the TAN(x) function a counterexample to this? Starting at a given point, it rises to infinity, then returns from negative infinity to the same point without ever having a slope of zero. [[Special:Contributions/172.68.58.89|172.68.58.89]] 06:58, 6 September 2018 (UTC)
:TAN(x) isn't differentiable at pi/2, hence the theorem doesn't apply--[[Special:Contributions/162.158.92.40|162.158.92.40]] 07:48, 6 September 2018 (UTC)
::And tan(x) has a slope of 0 at pi, so even if it applied, it wouldn't prove it wrong. A better example would be 1/x, but still invalid. [[User:Fabian42|Fabian42]] ([[User talk:Fabian42|talk]]) 08:01, 6 September 2018 (UTC)
:::Nope: tan(x) has a slope of 1 at pi, and its slope is never less than 1. Of course, that doesn't make it a counterexample. Zetfr 09:17, 6 September 2018 (UTC)

The math in the comic is well explained, but shouldn't there be something about the "math equivalent of the clueless art museum visitor..." part? Zetfr 09:17, 6 September 2018 (UTC)
** Seconded, all the argument here is about math that isn't even *in* the comic, where the bit that confuses me is the cultural metaphor[[Special:Contributions/162.158.154.235|162.158.154.235]] 07:16, 7 September 2018 (UTC)

Just so we're on the same page, while the proof of Rolle's theorem is not completely trivial, neither is it difficult by any means. Proving it seems to be a pretty common homework assignment in undergrad math classes, for example, so one might legitimately ask why it deserved to be named. Perhaps it's simply that it's old enough that the methods at the time were crappy, and so modern proofs are much easier. [[Special:Contributions/172.69.22.140|172.69.22.140]]
: It is named because it's a very important theorem in calculus, used to prove many other theorems or results. So when you need to prove something using this property, instead of re-demonstrating it or merely saying "it is well known that..." (which often raises alarm bells in the mind of the reader/corrector), all you have to do is reference Rolle's theorem.[[Special:Contributions/162.158.155.158|162.158.155.158]] 11:08, 6 September 2018 (UTC)
:: It could almost be called "Rolle's lemma". [[Special:Contributions/162.158.154.103|162.158.154.103]] 12:28, 6 September 2018 (UTC)
: When I am teaching Rolle's theorem, I always make it a point to draw the link to reals. Rolle's theorem fails when the output is complex valued. Then you can see for yourself how non-trivial this is. [[Special:Contributions/162.158.165.124|162.158.165.124]] 04:40, 7 September 2018 (UTC)

Has anyone else noted the irony of having a wiki page to explain a comic whose subject is how some things are self-evident? [[User:JamesCurran|JamesCurran]] ([[User talk:JamesCurran|talk]]) 20:13, 6 September 2018 (UTC)

Does the Kepler Conjecture actually belong on that list at the end? Most of the others are "derp" level intuitively obvious and/or essentially tautological on a very basic level, but the Kepler Conjecture couldn't actually be exhaustively proven until machine computation, nor is it intuitively definitive--if you've ever stacked round things into a box you've noticed that it feels like you're wasting a lot of space at the edges. So...? [[User:AtrumMessor|AtrumMessor]] ([[User talk:AtrumMessor|talk]]) 21:37, 6 September 2018 (UTC)

I also suggest that Fundamental Theorem of Calculus be removed from this list. Firstly, the beginner student, just introduced to derivatives and antiderivatives, will not easily see that antiderivatives are the same as finding areas under curves. Instead, it is only obvious upon hindsight, after instruction. More importantly, a restriction of the FTC to better-behaved spaces shows a far greater insanity: the restricted FTC is a consequence of generalised Stokes's theorem '''applied twice'''. This operation is so highly unintuitive, that one simply cannot claim that this is in any way, shape, or form, trivial. I think that trying to pretend that anything in beginning calculus is obvious to students is just going to alienate them rather than soothe their worries. [[Special:Contributions/162.158.165.124|162.158.165.124]] 04:40, 7 September 2018 (UTC)

"Munroe's theorem" should definitely refer to the circle thing in the alt text