explain xkcd - User contributions [en]

2347: Dependency

2024-04-28T20:44:14Z

Netjeff: /* Background and Examples */ Revised the xz example

{{comic
| number = 2347
| date = August 17, 2020
| title = Dependency
| image = dependency.png
| titletext = Someday ImageMagick will finally break for good and we'll have a long period of scrambling as we try to reassemble civilization from the rubble.
}}

==Explanation==
Technology architecture is often illustrated by a [https://www.guru99.com/images/1/102219_1135_TCPIPvsOSIM1.png stack diagram], in which higher levels of rectangles indicate components that are dependent on components in lower levels. This is analogous to a physical tower of blocks, in which higher blocks rest on lower blocks. The stack in this cartoon bears a striking resemblance to a physical block tower, suggesting the danger that the tower will lose its balance when a critical piece is removed, in this case a piece near the bottom, labeled as being maintained by a single semi-anonymous person located somewhere relatively unimportant doing it for their own unknown reasons without fame or acknowledgement. The concept of balance is not intended to be communicated by a stack diagram, making this a humorously absurd extension of a well-known diagram style.

{{w|ImageMagick}}, mentioned in the title text, is a popular, standalone utility released in 1990 that is used for performing transformations between various graphics file formats, and various other transformations. While there are also numerous libraries and APIs for performing these tasks within larger programs, ImageMagick is so popular and easy to use that many programs use its API or just find it easier to {{w|Shell (computing)#Other uses|shell out}} to ImageMagick to perform a necessary transformation. They therefore {{w|Dependency hell|depend}} on ImageMagick, and would break if ImageMagick were to disappear.

===Background and Examples===
Taking code re-usability and modularization to its logical extreme has been a long-time tenet for programmers; programming began as a slow task on very memory-constrained systems, utilizing punch cards and days of delay waiting to discover a bug, so that reuse made things possible that otherwise wouldn't be. Once systems became small, fast, and able to hold a lot of data, the ability to provide higher and higher degrees of automation made reusable libraries a huge engine behind the development of technology. By outsourcing what would seem like basic functions, such as string manipulation, to other libraries, developers waste less time reinventing the wheel, so the philosophy goes (or as Beret Guy's business practices literally: [[2140: Reinvent the Wheel]]), and thus many tiny packages, many of which contained only one function, became popular dependencies. This was especially true in Unix and Linux, where an entire program is commonly used for one small task, and programs exist to tie others together into powerful shell scripts.

Node.js (a platform for JavaScript) and Python are two modern ecosystems providing huge stashes of centralized libraries where developers of the world can come together to stand on the shoulders of all the small useful libraries they make for each other, to make new ones that are more and more powerful, and also more and more prone to sudden new unexpected bugs somewhere in the dependency chain. JavaScript was designed to be an easy to use front end scripting language, not a basic and core backend language as users of node.js's {{w|npm (software)|NPM}} package manager have made it be. While in theory, such a system may sound good for developers who would need to write and maintain fewer lines of code, systems which are highly optimized are also highly susceptible to rapid changes. For example, the famous left-pad incident in the NPM package manager left many major and minor web services which depended on it unable to build. [https://www.theregister.com/2016/03/23/npm_left_pad_chaos/ A disgruntled developer unpublishing 11 lines of code was able to break everybody's build, because everyone was using it.]

In 2014, the {{w|Heartbleed|Heartbleed bug}} revealed a significant portion of the internet was vulnerable to attack due to a bug in OpenSSL, a free and open-source library facilitating secure communication. One headline at the time demonstrated this comic in real life: [https://www.buzzfeed.com/chrisstokelwalker/the-internet-is-being-protected-by-two-guys-named-st "The Internet is Being Protected by Two Guys Named Steve"]. The aforementioned Steves were overworked, underfunded, and largely unknown volunteers whose efforts nevertheless underpinned the security of major websites throughout the world. Randall provided a concise, helpful explanation of the bug in [[1354: Heartbleed Explanation]].

In 2020, the sole maintainer of the library [https://github.com/zloirock/core-js/blob/master/docs/2023-02-14-so-whats-next.md core-js], used by 75% of the top 100 websites to polyfill in new JavaScript features for old browsers and depended on by tons of popular libraries such as Babel, ran over two dark-clothed drunk pedestrians, one of which were laying down, at night in Russia while speeding in front of a crossing. He quit previous jobs to be able to maintain core-js, resulting in not having enough money to settle, and he was convicted for 18 months in an open prison ([https://ru.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BB%D0%BE%D0%BD%D0%B8%D1%8F-%D0%BF%D0%BE%D1%81%D0%B5%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5 "колония-поселение"]).

Leading up to 2024, a user account going by the name Jia Tan gained the trust of ''{{w|XZ Utils|xz}}'''s (one and only) maintainer. Over the course of 3 years, Jia Tan cleverly inserted a patch into ''xz'' that allows a remote user to gain root-level access via the common ssh protocol. This {{w|XZ_Utils_backdoor|comprised version of ''xz''}} was released in March 2024. Another programmer, Andres Freund, found this backdoor before ''xz'' was widely distributed.

The current model of libraries and open-source development (topics which Randall has addressed extensively in the past) relies heavily on the free and continued dedication of unpaid hobbyists. Though some major projects such as Linux may be able to garner enough attention to build an organization, many smaller projects, which are in turn reused by larger projects, may only be maintained by one person, either the founder or another who has taken the torch. Maintaining libraries requires both extensive knowledge of the library itself as well as any use cases and the broader community around it, which usually is suited for maintainers who have spent years at the task, and thus cannot be easily replaced. Thus, there are many abandoned projects on the internet as people move on to greener pastures. Far from the days of backwards compatibility, that's usually not a problem, unless a project happens to be far up the dependency chain, as illustrated, in which case there may be a crisis down the road for both the developers and the users down the chain.

==Transcript==
:[A tower of blocks is shown. The upper half consists of many tiny blocks balanced on top of one another to form smaller towers, labeled:]
:All modern digital infrastructure

:[The blocks rest on larger blocks lower down in the image, finally on a single large block. This is balanced on top of a set of blocks on the left, and on the right, a single tiny block placed on its side. This one is labeled:]
:A project some random person in Nebraska has been thanklessly maintaining since 2003

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

2240: Timeline of the Universe

2023-04-01T16:52:24Z

Netjeff: /* Explanation */ Start Trek wikipedia links

{{comic
| number = 2240
| date = December 11, 2019
| title = Timeline of the Universe
| image = timeline_of_the_universe.png
| titletext = Not actual size, except technically at one spot near the left.
}}

==Explanation==

This comic is about the size of the {{w|visible universe}}, presented as a timeline in a way typical of representations of the {{w|timeline of epochs in cosmology}}.

Some events it describes, including the {{w|Big Bang}} and {{w|Inflation (cosmology)|Inflation}} are real, but others are jokes, including the ''Medium Bang'' and ''Settling''. The size history of the visible universe is also embellished for the sake of jokes; the actual size history of the universe has one period referred to as Inflation, which occurred shortly after the Big Bang, followed by comparatively gentle but accelerating expansion. This is artistically depicted in [https://map.gsfc.nasa.gov/media/060915/060915_CMB_Timeline150.jpg this image from NASA]. Part of the humor in this comic comes from the fact that the varied rate of change in expansion is not yet fully understood, with explanations of events leading to this change including theories such as "dark matter" and "dark energy" (this might therefore be construed as "dark humor"). At the end of the drawing four possible continuations of the timeline are suggested, with director J. J. Abrams listed as the deciding factor between them, stating that all future cosmological development has been handed over to him. Abrams directed the 2009 movie ''{{w|Star Trek (film)|Star Trek}}'', which established additional alternate timelines for the {{w|Star Trek|Star Trek franchise}}, so it may be implied that multiple timelines could result from direction by Abrams in the future. Notably, each Star Trek series has included multiple interacting timelines. For information about each of the events shown in this comic's ''Timeline of the Universe'', see detailed explanations in the section [[#Events on the Timeline of the Universe|Events on the Timeline of the Universe]] below.

The title text is a variation of one of [[Randall|Randall's]] standard jokes that his drawings are ''Not actual size''; in the case of this comic there is technically one spot near the left where the drawing depicts the actual relative size of the universe at the time the drawing represents. Where his drawing begins, at the time when the universe began, per definition, our visible universe had no measurable size. Very soon (within a tiny fraction of an attosecond) after the universe as we know it began, the inflation period blew it up very very fast and then it continued to expand until present day. So at some "time" after the big bang, our visible universe would have had a size (i.e. diameter) that would be the same as any thickness of Randall's universe "line". Since the universe as depicted in the comic goes from infinitesimal size at the moment of the Big Bang to the full size of the universe today, at some point near the left there will be a point where Randall's representation would have the same size as the universe at the correct "time period". Of course a problem with this is that there was only a very very short time period after inflation where the diameter of the observable universe is on the same scale as this comic, and that point is neither indicated nor likely to be accurate in relation to the duration of time elapsed. According to an answer given [https://physics.stackexchange.com/questions/32917/size-of-universe-after-inflation here] regarding the size of the visible universe after inflation, there is reason to believe that the size was still less than 1 mm in diameter when the stage of expansion known as Inflation ended, which is less than the thickness of the line shown at the Big Bang (depending on the screen size the comic is viewed upon); So the point along the timeline where the size of our visible universe matched the line width appears after the Inflation period is thought to have ended. Since Randall includes the ''Medium Bang'' before Inflation on his drawing he has already inserted a mistake there, but as the next three epochs after Inflation are real epochs, it is likely somewhere in this part of the drawing that the visible universe would have had the same diameter as the thickness of the drawing at a relevant time epoch on the drawing. This will thus not be that far to the left but around the Quark epoch.

===Events on the Timeline of the Universe===
The events presented in the timeline are:

* '''??''' (more than 13.8 billion years ago ({{w|Billion years|Gya}})): the unknown state of the universe prior to the Big Bang, if such a statement is even sensible. There are theories that our Universe is a bubble where inflation stopped (13.8 billion years ago in this universe) in an infinite and {{w|Eternal inflation|eternally inflating}} larger universe, which would give rise to the possibility of a {{w|multiverse}} with many bubble universes like ours where inflation has stopped. See for instance this recent video on the subject: [https://www.youtube.com/watch?v=XglOw2_lozc How Many Universes Are There?] from PBS Space Time. If this is true, the universe did not start at the big bang, but our part of the infinite universe actually began when the inflation period stopped, and not at the Big Bang.
* '''{{w|Big Bang}}''' (13.8 Gya): The model of the origin of the universe which has achieved consensus among astronomers. We have observed that all galaxies are receding away from Earth at rates that are roughly proportional to their distance, and the simplest explanation for this is that the universe is expanding. If the universe is expanding, then (unless new physics are discovered) it must have at one time been very, very small and dense; that moment in time is called the Big Bang.
* '''{{w|Timeline_of_epochs_in_cosmology#Planck_epoch|Planck Epoch}}''': The time period starting from the Big Bang, the Planck epoch or Planck era is the earliest stage of expansion currently calculable, before the time passed was equal to the Planck time (tP, or approximately 10^-43 seconds). There is no currently available physical theory to describe such short times, and it is not clear in what sense the concept of time is meaningful for values smaller than the Planck time.
* '''Medium Bang''' (a joke): If there's a Big Bang, why not have a medium one? There should probably also be a Little Bang, but maybe it's just too little to be featured on this chart.
* '''{{w|Inflation (cosmology)|Inflation}}''' (10^-36 to 10^-32 seconds after the Big Bang): A theory developed to explain the large-scale structure of the universe that postulates a period when the universe expanded very much faster than the speed of light. (The universe still expands faster than the speed of light, but only 2-3 times as fast. The limit of the speed c, is only valid for things moving in space time, not for the stretching of space itself!)
* '''{{w|Timeline_of_epochs_in_cosmology#Quarks_epoch|Quark Epoch}}''' (10^-12 seconds after the Big Bang): The universe is a quark-gluon plasma, up until 10^-6 seconds when it cools enough to coalesce into hadrons, including protons and neutrons.
* '''{{w|Timeline_of_epochs_in_cosmology#Lepton_epoch|Lepton Epoch}}''' (1 second after the Big Bang): Leptons, including electrons, and their associated neutrinos dominate.
* '''{{w|Timeline_of_epochs_in_cosmology#Photon_epoch|Photon Epoch}}''' (10 seconds after the Big Bang): The universe is dominated by photons.
* '''Cool Bug Epoch''' (a joke): There was a period around 10-17 million years after the Big Bang in which the cosmic background radiation was between 273 and 373 K, the temperature range for liquid water, but as oxygen had not yet been formed, as stars were not yet there to create it, there would have been no water. Cosmologists {{w|Avi_Loeb#Early_Universe|have speculated}} that primitive life could have arisen during this period and dubbed it the 'Habitable Epoch of the Early Universe', although it's unclear how this life would have formed since there was basically only hydrogen and helium atoms in the universe until the first Super Nova explosions some 100 million years later. Possibly this is the epoch in which the "cool red beetle" which [[Beret Guy]] added to his company's bug tracker (see [[1493: Meeting]]), or the "friendly bug" he wanted to show to a conference speaker (see [[2191: Conference Question]]), evolved.
* '''Molded grip''' (a joke): Some tools (e.g. knives) have molded finger-wells so that the user's hand settles easily and securely into a comfortable position. This epoch of the universe features repeated expansions and contractions so that this part of the timeline resembles a molded grip, at least in profile (it would be much too large to be held by any known animal's hands{{Citation needed}}, and the finger-wells are distributed over time as well as space).
* '''{{w|Timeline_of_epochs_in_cosmology#Cosmic_Dark_Age|Stars form}}''' (100 million years after the Big Bang): The universe cools enough to allow ordinary matter particles to group into stars.
* '''{{w|Stagflation}}''' (a joke): In addition to ''cosmic'' inflation, inflation can also refer to the economic phenomenon in which prices increase over time. Stagflation is a combination of the terms "stagnation" and "inflation", and refers to a situation in which monetary inflation is high, economic growth is slow, and job creation is low. This epoch of the universe shows the universe beginning to contract in size, much as economists would talk about an economy contracting.
* '''Settling''' (a joke): Thanks to government intervention and quantitative easing of the {{w|cosmological constant}}, or perhaps the judicious use of the Universe Control Panel, the contraction of the universe has halted. Alternately this may be a comparison to how in a package full of smaller items, the contents can "settle" over time so the empty space in between them is more filled in so it takes up less space overall leaving open space at the top (like how a cereal box may say "some settling may occur during shipment" to explain why the box doesn't seem completely full), and is thus claiming that somehow something similar to that decreased the size of the universe.
* '''Rebound''' (a joke): Consumer confidence has returned to the universe and it has begun expanding again. Alternatively, Settling and Rebound could be a reference to crustal rebound as the mere Earth occasionally shrinks and re-expands its surface. After all, Plate Tectonics games are fun when they are played in Real Time.
* '''Someone tripped and accidentally hit the "Inflation" switch again''' (a joke). This switch must be on the Universe Control panel referenced both in [[1620: Christmas Settings]] and in [[1763: Catcalling]].
* '''Emergency Stop triggered''' (a joke). Also on the Universe Control panel see previous entry.
* '''{{w|Timeline_of_epochs_in_cosmology#Galaxy_epoch|Galaxies form}}''' (12.8 Gya)
* '''{{w|Formation_and_evolution_of_the_Solar_System#Formation_of_the_planets|Earth forms}}''' (4.5 Gya)
* '''Present day'''
* '''Future cosmological development handed over to {{w|J.J. Abrams}}, outcome unknown''' (a joke): J.J. Abrams is a science-fiction writer and filmmaker. If he were in charge of the future development of the cosmos, he might decide to subject all of us to some strange plot twist. Among many other movies, he has directed the 2009 reboot of ''{{w|Star Trek (film)|Star Trek}}'', in which the "future history" of ''Star Trek'' is altered from the timeline of the original series by Nero and Spock traveling backwards in time. He also has directed other "Star" films, including ''{{w|Star Wars: The Force Awakens}}'' and ''{{w|Star Wars: The Rise of Skywalker}}'' (released a few weeks after the publishing of this comic) which altered the direction of ''Star Wars'' canon away from the post-film future laid out in the Expanded Universe publications. He is also involved in the {{w|Mission: Impossible (film series)|Mission: Impossible}} films.
**The dashed lines coming off the end of the timeline represent the possible fates of the universe:
*** The one curving in represents that the universe could stop expanding and begin contracting, resulting in the {{w|Big Crunch}}. In our universe, cosmological measurements have shown that the expansion of the universe is accelerating, so the Big Crunch is considered to be the least likely fate.
*** The second curve continuing the trend from before represents that the universe could settle into thermal equilibrium, which would leave no energy available for any interesting phenomena to occur. This is called the {{w|heat death of the universe}} or "Big Freeze".
*** The fourth curve represents that the universe's expansion will continue accelerating, eventually very rapidly, to the point that the accelerating expansion overcomes all forces between particles, turning the universe into a collection of particles isolated from each other by rapidly-expanding space. This is called the {{w|Big Rip}}.
***In between the second and fourth curve there seems to be something in between where the universe expansion accelerates and then slows down again. We have so far seen the expansion rate decelerate in the early life of the universe where the gravity of the more compact universe slowed the expansion, but then this turned around to an {{w|Timeline_of_epochs_in_cosmology#Acceleration|acceleration}} after about 9 billion years as the distance between galaxy clusters became so large that dark energy became the dominant force, causing the universe expansion to accelerate. So who knows if this could change again... At present our understanding says that the universe expansion-rate will keep accelerating. But left to J. J. Abrams, then the outcome is unknown. These four options represents both what we have theories for and what J. J. might come up with.

==Transcript==
:[A large header is above the main drawing:]
:<big>'''Timeline of the Universe'''</big>

:[The drawing shows a diagram of the evolution of the universe from the Big Bang (left) to the present right with lines indicating possible futures continuing right of the main drawing. The drawing is that of a black horn of plenty, very thin to the left and then it becomes broader, mainly in steps but also slightly between each step. n a few places the diameter decreases a bit. Along the "tube" are segments divided with thin white lines, with about equal distance between them. The first 20 the tube is black, but then stars form, shown as many white dots, and finally in the last 3-4 segments galaxies are shown. At the top and bottom of the opening to the right there are four dashed lines which behaves the same way. Two points inward, two continue the trend from before they begin, two goes out fast again, and then falls back to slow increase, and two goes almost straight up and down. At the far left there is a line going in to a small dot. On the line before the dot are two questions mark. A line points to the dot which has a starburst around it. It represents the Big Bang. After this firs labeled point on the drawing there are mange other labeled sections with a line going from the label to a segment on the drawing. There are 9 above, 9 below and one at each end. The one at the right end pointing to the four dashed future lines at the top. From left to right in the order they are labeled on the timeline, the labels are:]
:??
:Big Bang
:[The Universe comes in as a circle with action lines around it. It stays the same size for a while.]
:Planck Epoch
:Medium Bang
:[The Universe starts inflating very slowly]
:Inflation
:[The Universe briefly inflates very rapidly, and returns to its normal rate of expansion.]
:Quark Epoch
:Lepton Epoch
:Photon Epoch
:Cool Bug Epoch
:[The Universe starts inflating and deflating rapidly, forming a series of bumps in the universe diagram like the grip on a hand tool.]
:Molded grip
:[Stars appear in the timeline. The Universe starts inflating slightly faster than before.]
:Stars form
:Stagflation
:[The Universe starts deflating slowly.]
:Settling
:Rebound
:[The Universe starts inflating slowly again.]
:Someone tripped and accidentally hit the "Inflation" switch again
:[The Universe starts inflating at the same rate as the Inflation section.]
:Emergency Stop triggered
:[The Universe abruptly stops inflating, and stays level.]
:[Galaxies appear in the timeline. The Universe starts inflating at a medium pace.]
:Galaxies form
:Earth forms
:Present day
:[We see the edge of the Universe, with a rounded shape. Various dotted line predictions are on the edges.]
:Future Cosmological development handed over to J.J. Abrams, outcome unknown

{{comic discussion}}

[[Category:Charts]]
[[Category:Timelines]]
[[Category:Cosmology]]
[[Category:Astronomy]]
[[Category:Physics]]
[[Category:Animals]] 
[[Category:Comics featuring real people]]

2169: Predictive Models

2023-03-24T23:42:07Z

Netjeff: Add "Artificial Intelligence" category

{{comic
| number = 2169
| date = June 28, 2019
| title = Predictive Models
| image = predictive_models.png
| titletext = WE WILL ARREST THE REVOLUTION MEMBERS [AT THE JULY 28TH MEETING][tab] "Cancel the meeting! Our cover is blown."
}}

==Explanation==

{{w|Predictive text}} is a feature on many systems where as you type the system automatically suggests likely words or phrases to follow what you have written to that point. For instance, if you type "I'm heading" the system may suggest "home" or "back" as likely words to follow. Predictive systems usually use prior input to generate their predictions, so if you frequently type "Totally amazing!" the system will suggest "amazing!" every time you type "totally" even if you actually want to type "totally true" sometimes.

In the comic, [[Cueball]] is using predictive text to uncover a plot against his organization/government, but instead of using only his personal input, the system is using input from ''all'' users. By typing in an obscure phrase related to revolution and a meeting, he gets the predictive text algorithm to display where and when the next supposedly secret meeting will be held based on other users input. This works because it is unlikely that anyone else other than revolutionaries would be typing this phrase, thus the only data the algorithm has to predict from is the actual message from the revolutionaries on their next meeting. The caption of the comic is pointing out that systems which use prior input for predictive purposes in this way can end up leaking information that might otherwise be considered private. (However, this method may produce outdated information. On June 29, 2019, typing in Google "Long live the revolution. Our next meeting will be at" gave the predicted completion "long live the revolution. our next meeting will be at comic con 2018", which would not be useful information to anyone looking for revolutionaries, because Comic-Con 2018 was already over.)

The title text shows the revolutionaries using the same technique. By typing in "We will arrest the revolution members" they are hoping that the algorithm will suggest the time and date of their planned arrest, since no one other than the authorities would be typing in that phrase. Pressing the key [tab] to autocomplete that text produces "WE WILL ARREST THE REVOLUTION MEMBERS [AT THE JULY 28TH MEETING]", and the revolutionaries then say "Cancel the meeting! Our cover is blown." The revolutionaries have apparently made the serious mistake of holding secret meetings on regular, predictable dates (such as the 28th day of each month, the last date guaranteed to exist in any month of the Gregorian Calendar), and the authorities have successfully figured this out, either through the predictive-text attack or by other means.

Both examples assume that the revolutionaries and the authorities would be talking about very secret information in the clear on a network accessible to their adversaries. In the real world people engaged in sensitive activities would communicate via code, encryption, or both, or would do so through what they believe to be secure channels. There is still the danger of secret information leaking via non-secret channels, however.

{{w|Side-channel attack|Side-channel attacks}} use information gained from the implementation of a system to deduce supposedly protected information. A famous example occurred in World War II. The Germans kept tank production figures a secret, but they gave items like engine blocks sequential serial numbers. The Allies wanted to know exact tank production figures, so they solved the {{w|German tank problem}} by using statistical methods to analyze the distribution of these numbers on captured vehicles. They were able to predict tank production figures extremely accurately, to the point they predicted 270 tanks in a month when 276 were actually built. Thus the secret information on tank production leaked.

Some systems require frequent password change, in an effort to limit danger from a password being discovered. However, people respond by choosing passwords in patterns, so it is easy to predict what subsequent passwords will be, given old ones, thus defeating the purpose of requiring frequent changes.[https://www.troyhunt.com/passwords-evolved-authentication-guidance-for-the-modern-era/ Passwords Evolved: Authentication Guidance for the Modern Era]

Although the comic title is "Predictive Models", the term {{w|Predictive modelling}} usually refers to computer programs that try to predict outcomes from data aggregation, such as reviewing health records to identify people most at risk from certain diseases based on weight, prior injuries, etc., before testing directly for the diseases themselves. This is similar to but not precisely like the example in the comic, since predictive text is using direct input to predict further input, while predictive modelling is using related input (such as make and model of a car along with driver acceleration patterns) to predict a different output (such as likelihood of a crash). Both predictive text and predictive modelling could leak information as the comic suggests, however.

Predictive text and the possibility to leak unintended information has been parodied on xkcd before in [[1068: Swiftkey]].

==Transcript==
:[Cueball is sitting in an office chair at a desk typing on a laptop. Above him is the text he writes along with what the predictive text tool suggests, the latter in grey text. The TAB at the end is in a small frame.]
:Cueball typing: Long live the revolution. Our next meeting will be at| the docks at midnight on June 28 [tab]
:Cueball: ''Aha, found them!''

:[Caption below the panel:]
:When you train predictive models on input from your users, it can leak information in unexpected ways.

==Trivia==
*On its original release, the alt text was bugged. The full text would not display in certain browsers, and clicking the comic takes you to this page: [https://xkcd.com/%5BAT%2520THE%2520JULY%252028TH%2520MEETING%5D%5Btab%5D <nowiki>https://xkcd.com/[AT%20THE%20JULY%2028TH%20MEETING][tab]</nowiki>], which only shows "404 Not Found".
**The anchor actually contains invalid HTML <nowiki><a href=" [AT THE JULY 28TH MEETING][tab] "Cancel the meeting! Our cover is blown.""></nowiki>. This would suggest that [[Randall]] didn't intend this behaviour.
**The image and alt text were later corrected, long before July 28th, 2019, further implying it was a simple mistake on Randall's part.
*Some browsers, only show the first part of the title text "WE WILL ARREST THE REVOLUTION MEMBERS." For example Firefox version 66 Windows does this, evidently some versions of Firefox and chrome do likewise on GNU/Linux, also Windows 10 Microsoft Edge

{{comic discussion}}

[[Category:Artificial Intelligence]]
[[Category:Comics featuring Cueball]]

927: Standards

2022-10-01T16:30:51Z

Netjeff: /* Explanation */ rm extra space

{{comic
| number = 927
| date = July 20, 2011
| title = Standards
| image = standards.png
| titletext = Fortunately, the charging one has been solved now that we've all standardized on mini-USB. Or is it micro-USB? Shit.
}}

==Explanation==
For any engineering task, there are numerous ways a given problem can be solved. The more complex the task, the more room for diversity. That's all well and good for a one-off problem, but if a design is meant to be iterated over time, or if an entire industry is solving that same problem, part reuse and {{w|interoperability}} become issues to deal with. {{w|Technical standards}} thus came to exist so that industries could avoid wasting resources {{w|reinventing the wheel}}, whilst offering their clients a certain amount of simplicity and compatibility between vendors.

But, standards have issues of their own. They don't accommodate every {{w|Use Case|use case}}, they might have restrictions or royalties attached, and people tend to be plagued by ''{{w|Not invented here|Not Invented Here syndrome}}''. So, competing standards have a tendency to arise to address different perceived needs. After a while, the market for competing standards gets messy and hard to follow, and {{w|system integration|integrating systems}} built around competing standards gets burdensome. As a result, someone eventually takes on the challenge of creating a universal standard that everyone can rally around.

This almost never works. In many cases, a new standard fails to displace the incumbent standards, eventually loses funding and support, and thus becomes a relic of history. In many other cases, it only penetrates far enough to survive, ironically making the situation messier. The latter situation often ends up becoming cyclical, with new standards periodically rising and failing to gain traction.

Three examples are given at the top of the comic: {{w|AC adapter|AC chargers}}, {{w|character encoding}} and {{w|instant messaging}}.
* Power adapters are notorious for varying from device to device - partly to try to prevent dangerous voltage/current mismatches, but partly just because manufacturers all chose different adapter designs. Mobile phone chargers had mostly converged on a common USB-based solution, but laptop charging remained still a long way out, despite the adoption of yet another standard, {{w|IEC 62700}}, and current Apple iPhones now require "lightning" connectors and are not compatible with phone chargers using the USB-based solution. Randall notes that there was initially additional complexity due to the fact that there were also ''competing USB types'', but thanks to the European Union's {{w|common external power supply}} specification, micro-USB comprehensively won the day. Three years after the release of this comic, in August 2014 the {{w|USB Type-C}} specification was published and is currently displacing micro-USB, it's gaining ground among laptop manufacturers as well.
* Character encoding is, in theory, a solved problem - {{w|Unicode}} is a standard for character sets which currently includes over 135,000 characters. However, Unicode is not an encoding, just an abstract representation of the characters, and there are several implementations which encode Unicode "code points" into usable characters (including the two most common, {{w|UTF-8}} and {{w|UTF-16}}). Despite the [https://w3techs.com/technologies/history_overview/character_encoding/ms/y success of UTF-8 Unicode], older encodings like {{w|Windows-1252}} have stuck around, continuing to cause weird bugs in old software and websites to this day.
* Unlike the other examples, there has been little or no effort by instant messaging companies to make their services interoperable. There's more value to keeping IM as a {{w|closed platform}} so users are forced to use the company's software to access it. Some software, like the {{w|Trillian (software)|Trillian}} chat client, can connect to multiple different services, but there is essentially no way to, for example, send a Twitter message directly to a Skype user.

The title text mentions mini-USB and micro-USB, which were different standards used in 2011. As of 2019 for most applications of small USB ports (especially for charging / connecting cell phones), mini USB has lost most of its relevance and micro USB is competing with USB-C, as well as some solutions only used by single companies (such as Apple).

Not all {{w|technical standards|standards}} are created equal. In the development of {{w|technical standards|standards}}, private standards adopt a non-consensus process in comparison to voluntary consensus standards. Private standards in the {{w|Information and Communications Technology}} (ICT) sector and the agri-food industry (governed by the {{w|Global Food Safety Initiative}}) are discussed in a [https://docplayer.net/23885374-International-standards-and-private-standards.html publication from International Organization for Standardization.]

==Transcript==
:How Standards Proliferate
:(See: A/C chargers, character encodings, instant messaging, etc.)

:Situation:
:There are 14 competing standards.

:Cueball: 14?! Ridiculous! We need to develop one universal standard that covers everyone's use cases.
:Ponytail: Yeah!

:Soon:
:Situation: There are 15 competing standards.
{{comic discussion}}
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Ponytail]]

1047: Approximations

2022-10-01T16:28:45Z

Netjeff: /* Explanation */ For "white house" approximate value, increased to 13 digits

{{comic
| number = 1047
| date = April 25, 2012
| title = Approximations
| before = [[#Explanation|↓ Skip to explanation ↓]]
| image = approximations.png
| titletext = Two tips: 1) 8675309 is not just prime, it's a twin prime, and 2) if you ever find yourself raising log(anything)^e or taking the pi-th root of anything, set down the marker and back away from the whiteboard; something has gone horribly wrong.
}}

==Explanation==

This comic lists some approximations for numbers, most of them mathematical and physical constants, but some of them jokes and cultural references.

Approximations like these are sometimes used as {{w|mnemonic}}s by mathematicians and physicists, though most of Randall's approximations are too convoluted to be useful as mnemonics. Perhaps the best known mnemonic approximation (though not used here by Randall) is that "π is approximately equal to 22/7". Randall does mention (and mock) the common mnemonic among physicists that the {{w|fine structure constant}} is approximately 1/137. Although Randall gives approximations for the number of seconds in a year, he does not mention the common physicists' mnemonic that it is "π × 107", though he later added a statement to the top of the comic page addressing this point.

At the bottom of the comic are expressions involving {{w|transcendental numbers}} (namely π and e) that are tantalizingly close to being exactly true but are not (indeed, they cannot be, due to the nature of transcendental numbers). Such near-equations were previously discussed in [[217: e to the pi Minus pi]]. One of the entries, though, is a "red herring" that is exactly true.

Randall says he compiled this table through "a mix of trial-and-error, ''{{w|Mathematica}}'', and Robert Munafo's [http://mrob.com/pub/ries/ Ries] tool." "Ries" is a "{{w|Closed-form expression#Conversion from numerical forms|reverse calculator}}" that forms equations matching a given number.

The {{w|world population}} estimate for 2020 is still accurate. The estimate is 7.7 billion, and the population listed at the website census.gov is roughly the same. The current value can be found here: [https://www.census.gov/popclock/ United States Census Bureau - U.S. and World Population Clock]. Nevertheless there are other numbers listed by different sources.

The first part of the title text notes that "Jenny's constant," which is actually a telephone number referenced in Tommy Tutone's 1982 song {{w|867-5309/Jenny}}, is not only prime but a {{w|twin prime}} because 8675311 is also a prime. Twin primes have always been a subject of interest, because they are comparatively rare, and because it is not yet known whether there are infinitely many of them. Twin primes were also referenced in [[1310: Goldbach Conjectures]].

The second part of the title text makes fun of the unusual mathematical operations contained in the comic. {{w|Pi|π}} is a useful number in many contexts, but it doesn't usually occur anywhere in an exponent. Even when it does, such as with complex numbers, taking the πth root is rarely helpful. A rare exception is an [http://gosper.org/4%5E1%C3%B7%CF%80.png identity] for the pi-th root of 4 discovered by Bill Gosper. Similarly, {{w|e (mathematical constant)|e}} typically appears in the basis of a power (forming the {{w|exponential function}}), not in the exponent. (This is later referenced in [http://what-if.xkcd.com/73/ Lethal Neutrinos]).

{| class="wikitable"
|-
|align="center"|Thing to be approximated:
|align="center"|Formula proposed
|align="center"|Resulting approximate value
|align="center"|Correct value
|align="center"|Discussion
|-
|align="center"|One {{w|light year}} (meters)
|align="center"|998
|align="center"|9,227,446,944,279,201
|align="center"|9,460,730,472,580,800 (exact)
|align="left"|Based on 365.25 days per year (see below). 998 and 698 are [[487: Numerical Sex Positions|sexual references]].
|-
|align="center"|Earth's surface (m2)
|align="center"|698
|align="center"|513,798,374,428,641
|align="center"|5.10072 × 1014
|align="left"|998 and 698 are [[487: Numerical Sex Positions|sexual references]].
|-
|align="center"|Oceans' volume (m3)
|align="center"|919
|align="center"|1,350,851,717,672,992,089
|align="center"|1.332 × 1018
|align="left"|
|-
|align="center"|Seconds in a year
|align="center"|754
|align="center"|31,640,625
|align="center"|31,557,600 (Julian calendar), 31,556,952 (Gregorian calendar)
|align="left"|After this comic was released [[Randall]] got many responses by viewers. So he did add this statement to the top of the comic page:
"Lots of emails mention the physicist favorite, 1 year = pi × 107 seconds. 754 is a hair more accurate, but it's hard to top 3,141,592's elegance." π × 107 is nearly equal to 31,415,926.536, and 754 is exactly 31,640,625. Randall's elegance belongs to the number π, but it should be multiplied by the factor of ten.

Using the traditional definitions that a second is 1/60 of a minute, a minute is 1/60 of an hour, and an hour is 1/24 of a day, a 365-day common year is exactly 31,536,000 seconds (the "''Rent'' method" approximation) and the 366-day leap year is 31,622,400 seconds. Until the calendar was reformed by Pope Gregory, there was one leap year in every four years, making the average year 365.25 days, or 31,557,600 seconds. On the current calendar system, there are only 97 leap years in every 400 years, making the average year 365.2425 days, or 31,556,952 seconds. In technical usage, a "second" is now defined based on physical constants, even though the length of a day varies inversely with the changing angular velocity of the earth. To keep the official time synchronized with the rotation of the earth, a "leap second" is occasionally added, resulting in a slightly longer year.
|-
|align="center"|Seconds in a year (''Rent'' method)
|align="center"|525,600 × 60
|align="center"|31,536,000
|align="center"|31,557,600 (Julian calendar), 31,556,952 (Gregorian calendar)
|align="left"|"''Rent'' Method" refers to the song "{{w|Seasons of Love}}" from the musical ''{{w|Rent (musical)|Rent}}''. The song asks, "How do you measure a year?" One line says "525,600 minutes" while most of the rest of the song suggests the best way to measure a year is moments shared with a loved one.
|-
|align="center"|Age of the universe (seconds)
|align="center"|1515
|align="center"|437,893,890,380,859,375
|align="center"|(4.354 ± 0.012) × 1017 (best estimate; exact value unknown)
|align="left"|This one will slowly get more accurate as the universe ages.
|-
|align="center"|Planck's constant
|align="center"|<math>\frac {1} {30^{\pi^e}}</math>
|align="center"|6.6849901410 × 10−34
|align="center"|6.62606957 × 10−34
|align="left"|Informally, the {{w|Planck constant}} is the smallest action possible in quantum mechanics.
|-
|align="center"|Fine structure constant
|align="center"|<math>\frac{1}{140}</math>
|align="center"|0.00714285
|align="center"|0.0072973525664 (accepted value as of 2014), close to 1/137
|align="left"|The {{w|fine structure constant}} indicates the strength of electromagnetism. It is unitless and around 0.007297, close to 1/137. The joke here is that Randall chose to write 140 as the denominator, when 137 is much closer to reality and just as many digits (although 137 is a less "round" number than 140, and Randall writes in the table that he's "had enough" of it). At one point the fine structure constant was believed to be exactly the reciprocal of 137, and many people have tried to find a simple formula explaining this (with a pinch of {{w|numerology}} thrown in at times), including the infamous {{w|Arthur Eddington|Sir Arthur "Adding-One" Eddington}} who argued very strenuously that the fine structure constant "should" be 1/136 when that was what the best measurements suggested, and then argued just as strenuously for 1/137 a few years later as measurements improved.
|-
|align="center"|Fundamental charge
|align="center"|<math>\frac {3} {14 \pi^{\pi^\pi}}</math>
|align="center"|1.59895121062716 × 10−19
|align="center"|1.602176565 × 10−19
|align="left"|This is the charge of the proton, symbolized ''e'' for electron (whose charge is actually −''e''. You can blame Benjamin Franklin [[567|for that]].)
|-
|align="center"|Telephone number for the {{w|White House}} switchboard
|align="center"|<math>\frac {1} {e^ {\sqrt[\pi] {1 + \sqrt[e-1] 8}} }</math>
|align="center"|0.2024561414932
|align="center"|202-456-1414
|align="left"|
|-
|align="center"|Jenny's constant
|align="center"|<math>\left( 7^ {\frac{e}{1} - \frac{1}{e}} - 9 \right) \pi^2</math>
|align="center"|867.5309019
|align="center"|867-5309
|align="left"|A telephone number referenced in {{w|Tommy Tutone}}'s 1982 song {{w|867-5309/Jenny}}. As mentioned in the title text, the number not only prime but a {{w|twin prime}} because 8675311 is also a prime.
|-
|align="center"|World population estimate (billions)
|align="center"|Equivalent to <math>6 + \frac {\frac34 y + \frac14 (y \operatorname{mod} 4) - 1499} {10}</math>
|align="center"|2005 — 6.5 
2006 — 6.6 
2007 — 6.7 
2008 — 6.7 
2009 — 6.8 
2010 — 6.9 
2011 — 7.0 
2012 — 7.0 
2013 — 7.1 
2014 — 7.2 
2015 — 7.3 
2016 — 7.3 
2017 — 7.4 
2018 — 7.5 
2019 — 7.6 
2020 — 7.6 
2021 — 7.7 
2022 — 7.8 
2023 — 7.9 
2024 — 7.9 
2025 — 8.0 
2026 — 8.1 
2027 — 8.2 
2028 — 8.2 
2029 — 8.3 
2030 — 8.4 
2031 — 8.5 
|align="center"|
|align="left"|Grows by 75 million every year on average. As of 2021, a little too small.
|-
|align="center"|U.S. population estimate (millions)
|align="center"|Equivalent to <math>310 + 3(y - 2010)</math>
|align="center"|2000 — 280 
2001 — 283 
2002 — 286 
2003 — 289 
2004 — 292 
2005 — 295 
2006 — 298 
2007 — 301 
2008 — 304 
2009 — 307 
2010 — 310 
2011 — 313 
2012 — 316 
2013 — 319 
2014 — 322 
2015 — 325 
2016 — 328 
2017 — 331 
2018 — 334 
2019 — 337 
2020 — 340 
2021 — 343 
2022 — 346 
2023 — 349 
2024 — 352 
2025 — 355 
2026 — 358 
2027 — 361 
2028 — 364 
2029 — 367 
2030 — 370 
2031 — 373 
2032 — 376
|align="center"|
|align="left"|Grows by 3 million each year. As of 2021 the actual number is ~13 million smaller.
|-
|align="center"|Electron rest energy (joules)
|align="center"|<math>\frac {e} {7^{16}}</math>
|align="center"|8.17948276564429 × 10−14
|align="center"|8.18710438 × 10−14
|align="left"|
|-
|align="center"|Light year (miles)
|align="center"|242.42
|align="center"|5,884,267,614,436.97
|align="center"|5,878,625,373,183.61 = 9,460,730,472,580,800 (meters in a light-year, by definition) / 1609.344 (meters in a mile)
|align="left"|{{w|42 (number)|42}} is, according to {{w|Douglas Adams}}' ''{{w|The Hitchhiker's Guide to the Galaxy}}'', the answer to the Ultimate Question of Life, the Universe, and Everything.
|-
|align="center"|<math>\sin\left(60^\circ\right) = \frac {\sqrt 3} {2}</math>
|align="center"|<math>\frac{e}{\pi}</math>
|align="center"|0.8652559794
|align="center"|0.8660254038
|align="left"|
|-
|align="center"|<math>\sqrt 3</math>
|align="center"|<math>\frac{2e}{\pi}</math>
|align="center"|1.7305119589
|align="center"|1.7320508076
|align="left"|Same as the above
|-
|align="center"|γ (Euler's gamma constant)
|align="center"|<math>\frac {1} {\sqrt 3}</math>
|align="center"|0.5773502692
|align="center"|0.5772156649
|align="left"|The {{w|Euler–Mascheroni constant}} (denoted γ) is a mysterious number describing the relationship between the {{w|Harmonic series (mathematics)|harmonic series}} and the {{w|natural logarithm}}.
|-
|align="center"|Feet in a meter
|align="center"|<math>\frac {5} {\sqrt[e]\pi}</math>
|align="center"|3.2815481951
|align="center"|3.280839895
|align="left"|Exactly 1/0.3048, as the {{w|international foot}} is defined as 0.3048 meters.
|-
|align="center"|<math>\sqrt 5</math>
|align="center"|<math>\frac{2}{e} + \frac32</math>
|align="center"|2.2357588823
|align="center"|2.2360679775
|align="left"|
|-
|align="center"|Avogadro's number
|align="center"|<math>69^{\pi^\sqrt{5}}</math>
|align="center"|6.02191201246329 × 1023
|align="center"|6.02214129 × 1023
|align="left"|Also called a mole for shorthand, {{w|Avogadro's number}} is (roughly) the number of individual atoms in 12 grams of pure carbon. Used in basically every application of chemistry. In 2019 the constant was redefined to 6.02214076 × 1023, making the Approximation slightly more correct.
|-
|align="center"|Gravitational constant ''G''
|align="center"|<math>\frac {1} {e ^ {(\pi-1)^{(\pi+1)}}}</math>
|align="center"|6.6736110685 × 10−11
|align="center"|6.67385 × 10−11
|align="left"|The universal {{w|gravitational constant}} G is equal to ''Fr''2/''Mm'', where ''F'' is the gravitational force between two objects, ''r'' is the distance between them, and ''M'' and ''m'' are their masses.
|-
|align="center"|''R'' (gas constant)
|align="center"|<math>(e + 1) \sqrt 5</math>
|align="center"|8.3143309279
|align="center"|8.3144622
|align="left"|The {{w|gas constant}} relates energy to temperature in physics, as well as a gas's volume, pressure, temperature and {{w|mole (unit)|molar amount}} (hence the name).
|-
|align="center"|Proton–electron mass ratio
|align="center"|<math>6 \pi^5</math>
|align="center"|1836.1181087117
|align="center"|1836.15267246
|align="left"| The {{w|proton-to-electron mass ratio}} is the ratio between the rest mass of the proton divided by the rest mass of the electron.
|-
|align="center"|Liters in a {{w|gallon}}
|align="center"|<math>3 + \frac{\pi}{4}</math>
|align="center"|3.7853981634
|align="center"|3.785411784 (exact)
|align="left"|A U.S. liquid gallon is defined by law as 231 cubic inches
|-
|align="center"|''g''0 or ''g''n
|align="center"|6 + ln(45)
|align="center"|9.8066624898
|align="center"|9.80665
|align="left"|Standard gravity, or standard acceleration due to free fall is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is defined by standard as 9.80665 m/s2, which is exactly 35.30394 km/h/s (about 32.174 ft/s2, or 21.937 mph/s). This value was established by the 3rd CGPM (1901, CR 70) and used to define the standard weight of an object as the product of its mass and this nominal acceleration. The acceleration of a body near the surface of the Earth is due to the combined effects of gravity and centrifugal acceleration from rotation of the Earth (but which is small enough to be neglected for most purposes); the total (the apparent gravity) is about 0.5 percent greater at the poles than at the equator.

Randall used a letter ''g'' without a suffix, which can also mean the local acceleration due to local gravity and centrifugal acceleration, which varies depending on one's position on Earth.
|-
|align="center"|Proton–electron mass ratio
|align="center"|<math>\frac {e^8 - 10} {\phi}</math>
|align="center"|1836.1530151398
|align="center"|1836.15267246
|align="left"|φ is the {{w|golden ratio}}, or <math>\textstyle{ \frac{1+\sqrt 5}{2} }</math>. It has many interesting geometrical properties.
|-
|align="center"|Ruby laser wavelength (meters)
|align="center"|<math>\frac{1}{1200^2}</math>
|align="center"|6.9444 × 10−7
|align="center"|~6.943 × 10−7
|align="left"|The {{w|ruby laser}} wavelength varies because "ruby" is not clearly defined.
|-
|align="center"|Mean Earth radius (meters)
|align="center"|<math>5^8 6e</math>
|align="center"|6,370,973.035
|align="center"|6,371,008.7 (IUGG definition)
|align="left"|The {{w|Earth radius#mean radii|mean earth radius}} varies because there is not one single way to make a sphere out of the earth. Randall's value lies within the actual variation of Earth's radius. The International Union of Geodesy and Geophysics (IUGG) defines the mean radius as 2/3 of the equatorial radius (6,378,137.0 m) plus 1/3 of the polar radius (6,356,752.3 m).
|-
|align="center"|<math>\sqrt 2</math>
|align="center"|<math>\frac35 + \frac{\pi}{7-\pi}</math>
|align="center"|1.4142200581
|align="center"|1.4142135624
|align="left"|There are recurring math jokes along the lines of, "<math>\textstyle{ \frac35 + \frac{\pi}{7-\pi} - \sqrt{2} = 0}</math>, but your calculator is probably not good enough to compute this correctly". See also [[217: e to the pi Minus pi]].
|-
|align="center"|<math>\cos \frac{\pi}{7} + \cos \frac{3\pi}{7} + \cos \frac{5\pi}{7}</math>
|align="center"|<math>\frac12</math>
|align="center"|0.5
|align="center"|0.5 (exact)
|align="left"|This is the exactly correct equation referred to in the note, "Pro tip – Not all of these are wrong", as shown below and also [http://math.stackexchange.com/questions/140388/how-can-one-prove-cos-pi-7-cos3-pi-7-cos5-pi-7-1-2 here]. If you're still confused, the functions use {{w|radians}}, not {{w|degrees (angle)|degrees}}.
|-
|align="center"|γ (Euler's gamma constant)
|align="center"|<math>\frac{e}{3^4} + \frac{e}{5}</math>
|align="center"|0.5772154006
|align="center"|0.5772156649
|align="left"|The {{w|Euler–Mascheroni constant}} (denoted γ) is a mysterious number describing the relationship between the {{w|Harmonic series (mathematics)|harmonic series}} and the {{w|natural logarithm}}.
|-
|align="center"|<math>\sqrt 5</math>
|align="center"|<math>\frac {13+4\pi} {24-4\pi}</math>
|align="center"|2.2360678094
|align="center"|2.2360679775
|align="left"|
|-
|align="center"|<math>\sum_{n=1}^{\infty} \frac{1}{n^n}</math>
|align="center"|<math>\ln(3)^e</math>
|align="center"|1.2912987577
|align="center"|1.2912859971
|align="left"|
|}

===Proof===

One of the "approximations" actually is precisely correct: <math>\textstyle{ \cos \frac{\pi}{7} + \cos \frac{3\pi}{7} + \cos \frac{5\pi}{7} = \frac12 }</math>. Here is a proof:

:<math>\cos \frac{\pi}{7} + \cos \frac{3\pi}{7} + \cos \frac{5\pi}{7}</math>

Multiplying by 1 (or by a nonzero number divided by itself) leaves the equation unchanged:

:<math>= \left( \cos \frac{\pi}{7} + \cos \frac{3\pi}{7} + \cos \frac{5\pi}{7} \right) \frac{2 \sin\frac{\pi}{7}}{2 \sin\frac{\pi}{7}}</math>

The <math>\textstyle{ 2 \sin\frac{\pi}{7} }</math> on the top of the fraction is multiplied through the original equation:

:<math>= \frac {2 \cos \frac{\pi}{7} \sin\frac{\pi}{7} + 2 \cos \frac{3\pi}{7} \sin\frac{\pi}{7} + 2 \cos \frac{5\pi}{7} \sin\frac{\pi}{7}} {2 \sin\frac{\pi}{7}}</math>

Use the trigonometric identity <math>\textstyle{ 2 \cos A \sin B = \sin (A+B) - \sin(A-B)}</math> on the second and third terms in the numerator:

:<math>\begin{align}
&= \frac {2 \cos \frac{\pi}{7} \sin \frac{\pi}{7} + \left[\sin \left(\frac{3\pi}{7} + \frac{\pi}{7}\right) - \sin \left(\frac{3\pi}{7} - \frac{\pi}{7}\right) \right] + \left[\sin \left(\frac{5\pi}{7} + \frac{\pi}{7}\right) - \sin \left(\frac{5\pi}{7} - \frac{\pi}{7}\right) \right]} {2 \sin\frac{\pi}{7}} \\
&= \frac {2 \cos \frac{\pi}{7} \sin \frac{\pi}{7} + \left[\sin \frac{4\pi}{7} - \sin \frac{2\pi}{7} \right] + \left[\sin \frac{6\pi}{7} - \sin \frac{4\pi}{7} \right]} {2 \sin\frac{\pi}{7}}
\end{align}</math>

Use the trigonometric identity <math>\textstyle{ 2 \cos A \sin A = \sin 2A }</math> on the first term in the numerator:

:<math>\begin{align}
&= \frac {\sin \frac{2\pi}{7} + \left[\sin \frac{4\pi}{7} - \sin \frac{2\pi}{7} \right] + \left[\sin \frac{6\pi}{7} - \sin \frac{4\pi}{7} \right]} {2 \sin\frac{\pi}{7}} \\
&= \frac {\sin \frac{6\pi}{7} + \left[\sin \frac{4\pi}{7} - \sin \frac{4\pi}{7} \right] + \left[\sin \frac{2\pi}{7} - \sin \frac{2\pi}{7} \right]} {2 \sin\frac{\pi}{7}} \\
&= \frac {\sin \frac{6\pi}{7} } {2 \sin\frac{\pi}{7}}
\end{align}</math>

Noting that <math>\textstyle{\frac{6\pi}{7} + \frac{\pi}{7} = \pi}</math> and that the sines of supplementary angles (angles that sum to π) are equal:

:<math>\begin{align}
&= \frac {\sin \frac{\pi}{7} } {2 \sin\frac{\pi}{7}} \\
&= \frac12 \quad \quad \quad \text{Q.E.D.}
\end{align}</math>

==Transcript==
:'''A table of slightly wrong equations and identities useful for approximations and/or trolling teachers.'''
:(Found using a mix of trial-and-error, ''Mathematica'', and Robert Munafo's ''Ries'' tool.)
: All units are SI MKS unless otherwise noted.

:{| class="wikitable"
|-
|colspan="2" align="center" | Relation:
|align="center" | Accurate to within:
|-
|align="center" | One light-year(m)
|align="center" | 998
|align="center" | one part in 40
|-
|align="center" | Earth Surface(m2)
|align="center" | 698
|align="center" | one part in 130
|-
|align="center" | Oceans' volume(m3)
|align="center" | 919
|align="center" | one part in 70
|-
|align="center" | Seconds in a year
|align="center" | 754
|align="center" | one part in 400
|-
|align="center" | Seconds in a year (''Rent'' method)
|align="center" | 525,600 x 60
|align="center" | one part in 1400
|-
|align="center" | Age of the universe (seconds)
|align="center" | 1515
|align="center" | one part in 70
|-
|align="center" | Planck's constant
|align="center" | 1/(30πe)
|align="center" | one part in 110
|-
|align="center" | Fine structure constant
|align="center" | 1/140
|align="center" | [I've had enough of this 137 crap]
|-
|align="center" | Fundamental charge
|align="center" | 3/(14 * πππ)
|align="center" | one part in 500
|-
|align="center"|White House Switchboard
|colspan="2" align="center"|1 / (eπ√(1 + (e-1)√8))
|-
|align="center"|Jenny's Constant
|colspan="2" align="center"|(7(e/1 - 1/e) - 9) * π2
|-
|colspan="3" align="center"|Intermission: World Population Estimate which should stay current for a decade or two: 
Take the last two digits of the current year

Example: 20[14]

Subtract the number of leap years since hurricane Katrina

Example: 14 (minus 2008 and 2012) is 12

Add a decimal point

Example: 1.2

Add 6

Example: 6 + 1.2

7.2 = World population in billions.

Version for US population:

Example: 20[14]

Subtract 10

Example: 4

Multiply by 3

Example: 12

Add 10

Example: 3[22] million
|-
|align="center"|Electron rest energy
|align="center"|e/716 J
|align="center"|one part in 1000
|-
|align="center"|Light-year(miles)
|align="center"|2(42.42)
|align="center"|one part in 1000
|-
|colspan="2" align="center"|sin(60°) = √3/2 = e/π
|align="center"|one part in 1000
|-
|colspan="2" align="center"|√3 = 2e/π
|align="center"|one part in 1000
|-
|align="center"|γ(Euler's gamma constant)
|align="center"|1/√3
|align="center"|one part in 4000
|-
|align="center"|Feet in a meter
|align="center"|5/(e√π)
|align="center"|one part in 4000
|-
|colspan="2" align="center"|√5 = 2/e + 3/2
|align="center"|one part in 7000
|-
|align="center"|Avogadro's number
|align="center"|69π√5
|align="center"|one part in 25,000
|-
|align="center"|Gravitational constant G
|align="center"|1 / e(π - 1)(π + 1)
|align="center"|one part in 25,000
|-
|align="center"|R (gas constant)
|align="center"|(e+1) √5
|align="center"|one part in 50,000
|-
|align="center"|Proton-electron mass ratio
|align="center"|6*π5
|align="center"|one part in 50,000
|-
|align="center"|Liters in a gallon
|align="center"|3 + π/4
|align="center"|one part in 500,000
|-
|align="center"|g
|align="center"|6 + ln(45)
|align="center"|one part in 750,000
|-
|align="center"|Proton-electron mass ratio
|align="center"|(e8 - 10) / ϕ
|align="center"|one part in 5,000,000
|-
|align="center"|Ruby laser wavelength
|align="center"|1 / (12002)
|align="center"|[within actual variation]
|-
|align="center"|Mean Earth Radius
|align="center"|(58)*6e
|align="center"|[within actual variation]
|-
|colspan="3" align="center"|Protip - not all of these are wrong:
|-
|colspan="2" align="center"|√2 = 3/5 + π/(7-π)
|align="center"|cos(π/7) + cos(3π/7) + cos(5π/7) = 1/2
|-
|align="center"|γ(Euler's gamma constant) = e/34 + e/5
|align="center"|√5 = (13 + 4π) / (24 - 4π)
|align="center"|Σ 1/nn = ln(3)e
|}

{{comic discussion}}
[[Category:Charts]]
[[Category:Math]]
[[Category:Physics]]
[[Category:Protip]]

2511: Recreate the Conditions

2021-09-08T06:53:10Z

Netjeff: /* Explanation */ typo

{{comic
| number = 2511
| date = September 3, 2021
| title = Recreate the Conditions
| image = recreate_the_conditions.png
| titletext = We've almost finished constructing the piña collider.
}}

==Explanation==
{{incomplete|Created by a BIG BANG FLAVORED PIÑA COLLIDER. Do NOT delete this tag too soon.}}

Scientists recreate conditions of things to gain scientific knowledge on a topic to better be able to observe why or how things happen. This could be done by making miniature versions of events and simulating events using safe methods.

In this comic, [[Megan]]'s lab discovered that the conditions during the seconds after the {{w|Big Bang}} were extremely hot and unpleasant. They have thus decided to attempt to recreate the conditions of a {{w|tropical}} {{w|beach}} in 2014 instead (7 years prior to when this comic was released). Here, the joke is that instead of recreating a condition for scientific study purposes, Megan and her crew were simply trying to create a pleasant environment for recreation, in the sense of personal enjoyment.

The title text is a reference to [[1949: Fruit Collider]] a pun of {{w|piña colada}} (Spanish for "strained Pineapple") and a particle {{w|collider}}: the Spanish word "colada" is pronounced similarly to the English word "collider". Taken literally, "piña collider" would be a pineapple collider, which may be interpreted as a fruit juicing machine for making piña coladas.

==Transcript==
:[Megan is standing, pointing a stick at a poster of a particle collision, (as it looks when measured in a particle collider), where many other particles emerge from the central collision, a black spot, with many thin curved lines going away from it, and two larger beams going straight in. Above the upper part of these lines there are three lines of unreadable text, three unreadable labels are written over three of the lines, and there are two unreadable lines of text at the bottom one at each side of the poster.]
:Megan: Our lab was trying to recreate the conditions that occurred seconds after the Big Bang.

:[Megan is standing with arms lifted to each side, stick in hand, looking straight out, in an otherwise empty panel.]
:Megan: But it turns out they were ''extremely'' hot and unpleasant.

:[Megan points at another poster with the stick. The poster shows a picture of a beach, with the sun over the ocean, a palm tree bending in over a parasol stuck in the sand. At the front there is a small table with two drinks on it.]
:Megan: So now we're trying to recreate the conditions that occurred on this tropical beach in early 2014.
:Megan: Honestly don't know why we were doing that other thing.

{{comic discussion}}

[[Category:Comics featuring Megan]]
[[Category:Astronomy]]
[[Category:Physics]]
[[Category:Food]]
[[Category:Puns]]

2251: Alignment Chart Alignment Chart

2021-01-07T02:50:54Z

Netjeff: Link to 2408: Egg Strategies

{{comic
| number = 2251
| date = January 6, 2020
| title = Alignment Chart Alignment Chart
| image = alignment_chart_alignment_chart.png
| titletext = I would describe my personal alignment as "lawful heterozygous silty liquid."
}}

==Explanation==
"Alignment" and "alignment charts" come from tabletop roleplaying games, most prominently ''{{w|Dungeons & Dragons}}''. Every character has an {{w|Alignment (Dungeons & Dragons)|alignment}}, which very roughly identifies their tendencies. The most widely used alignment system was introduced in the ''{{w|Dungeons & Dragons Basic Set}}'' in 1977 and has been reused in many (but not all) subsequent editions of the game. This system uses two perpendicular axes, each divided into three levels (for a total of nine categories). The two axes are:
* Lawful/neutral/chaotic: this axis says whether a character is strongly devoted to, indifferent about, or categorically opposed to following established rules.
* Good/neutral/evil: this axis says whether a character is generally inclined to commit good deeds or evil deeds.

In this system, the "lawful" attribute is independent from the "good" attribute. Lawful alignment means that a character is committed to a set of rules, which can refer to actual established laws, or to something like a rigid personal code, a set of traditions, or a chain of command, while a chaotic alignment means that a character has no interest in those, and may actively oppose them. The good vs evil scale is generally based on a character's concern for the lives and well-being of others, a good character will actively seek to help others and prevent harm, while an evil character will have no such concern and may actively harm others. Being 'good' is assumed to be independent of being 'lawful'. For example, a character who actively breaks laws to help those who are unjustly imprisoned or oppressed would be be considered to be "chaotic good". In both cases, a neutral alignment can indicate a character's indifference to a concept, or that their commitment is conditional, or that they consciously seek to balance both sides. A character with the "neutral neutral" alignment is called a true neutral.

An alignment chart is a grid that divides the alignments, usually for the purpose of putting descriptions or particular characters on it. Alignment charts are frequently used as a [https://knowyourmeme.com/memes/mcdonalds-alignment-chart meme template], where humorous or absurdist things are organized into different alignments. In addition to the "classic" Dungeons and Dragons alignment chart, there are a number of variant alignment charts in use as meme templates. Many keep the three-by-three grid structure but replace the lawful-neutral-chaotic and good-neutral-evil axes with descriptions.

This comic claims to be a meta-alignment chart, where nine "alignment charts" are themselves sorted into the nine Dungeons and Dragons alignments, following the use of alignment charts to humorously classify abstract concepts. However, these "alignment charts" are mostly diagrams used in academic classifications, which are being treated as if they were blank meme templates. There are two levels of absurdity here: first, the idea of using these diagrams to classify things they were never intended for, and second, the conflation of chaos as a physics concept and an assigned moral weight as it applies to each of these classification systems.

The title text describes Randall's alignment as "lawful heterozygous silty liquid" which references the true neutral, neutral good, lawful good, and lawful neutral charts in the Alignment Chart Alignment Chart. Lawful is the left side of an alignment chart, heterozygous is the top right or bottom left of a Punnet Square, silty is the bottom right of a soil chart, and liquid is the top right of a phase diagram. As such, the title text describes Randall's alignment as between Lawful Neutral and Neutral Good on this chart.

{| class="wikitable"
!Alignment
!Chart
!Explanation
|-
|Lawful Good
|{{w|Soil texture|Soil chart}}
|This chart shows the USDA classification of soil types by their relative proportions of sand, clay and silt. The chart is a ternary diagram (very common in geology), so soils with more clay plot towards the upper corner, soils with more sand to the bottom left, and soils with more silt to the bottom right. This chart has been used humorously as an alignment chart ([https://www.reddit.com/r/PrequelMemes/comments/8wakd4/anakin_soil_reference_chart/ for example]) and may have been the inspiration for Randall to use scientific diagrams as alignment charts. In addition to being Lawful Good, this grid cell is also the upper left cell of the chart and will be read first, making it a good place to put this chart as a "jumping off point". [https://what-if.xkcd.com/83/ What If 83 "Star Sand"] cites Randall as "...very satisfied with this chart, it's like the erosion geology edition of the electromagnetic spectrum chart..."
|-
|Neutral Good
|{{w|Punnett square}}
| Punnet squares are a visual method of determining what traits an organism might have based on the traits of the organism's parents. It relies on the principle that a trait is either dominant (indicated with capital letters) or recessive (indicated with lowercase letters). The exact combination of dominant or recessive genes that a child organism receives from their parents determines their traits. Heterozygous and homozygous refers to the pairs of alleles in an organism’s genotype, indicating mixed or same alleles, respectively. Randall later uses "heterozygous" in the title text. Note that it is possible for a phenotype to be expressed the same between some heterozygotes and homozygotes, e.g., persons with genotypes heterozygous "Aa" and homozygous "AA" will both express blood type A.
Therefore, the Punnett Square is a good chart because it is both a simple and true geometric predictor of inheritance, but it tends to be neutral because of complicating factors such as polygenic inheritance; these and other factors will cause genotypic frequency to deviate from expected 1:2:1 patterns.
|-
|Chaotic Good
|{{w|IPA vowel chart with audio|IPA vowel chart }}
|This chart shows the relationship between different vowels according to the {{w|International Phonetic Alphabet}}. The position of the vowel on the chart serves roughly as an indicator of the position of the tongue in the mouth of the speaker. As different vowel sounds are created by changes in different parts of the mouth, including lip roundness which is expressed in the chart implicitly as an invisible third dimension, vowel identification is qualitative and often up to interpretation, and vowel expression can change dramatically from region to region or even person to person within the same language, the categories described by the chart might be considered chaotic. The chart is missing the near-open central vowel [ɐ] and the open central vowel [ä] (often written as /a/).
|-
|Lawful Neutral
|{{w|Phase diagram}}
|A phase diagram shows the equilibrium phases of matter present for a particular temperature, pressure, and composition. The diagram included is a unary phase diagram of a typical material that has a solid, liquid, and gas phase depending on the temperature and pressure for a fixed composition. Phase diagrams are useful for understanding how a material may change as its conditions change. For example, the air pressure of Mars is such that there is no temperature at which liquid water can exist in equilibrium on its surface. Water exists as ice until the temperature reaches a point where it sublimates directly into steam.

This phase diagram does not specify what material is depicted, but it is certainly ''not'' the phase diagram of water. On this diagram, compressing the liquid phase will transform the material into a solid, which is how most materials behave, but the solid/liquid phase line for water tilts the opposite direction. This is why water ice floats on liquid water, for example.

Phase diagrams follow the laws of thermodynamics and concern themselves with the order in which things ''should'' be, so they are inherently lawful.
|-
|True Neutral
|Alignment chart
|All alignment charts are neutral unless humans contaminate them. The chart in this cell has the same overall shape as the Alignment Chart Alignment Chart in the comic.
|-
|Chaotic Neutral
|CIE chromaticity diagram
|The {{w|chromaticity}} diagram is a chart of colors. Visible colors form a shape like a triangle with two bulging sides in the diagram. The curved line within the diagram shows the chromaticities of {{w|Black body|black bodies}} over a range of color temperatures. The chromaticity diagram shows colors independent of luminance.
The chart is not a simple geometric shape, so it is labeled as chaotic. Points on the diagram can be specified as combinations of three underlying iluminants (the colors of which may not all be visible). It can also be described in polar form with angle and radial distance from some central point, where the maximum radial distance depends on the angle.
The fact that the colors may not show properly on a screen, making the diagram incorrect, may also contribute to its chaotic aspect, as well as the fact that the official standard is behind a paywall.
|-
|Lawful Evil
|Political compass
|[https://www.politicalcompass.org/ Political Compass] separates ideas about governance into economic and social political thought. For example, Gandhi and Stalin supposedly both had similar economic perspectives (collectivist) but radically different social perspectives (libertarian vs authoritarian).

As politics is how laws are made, this is inherently lawful. Representing all politics in terms of two very general axes is not only a gross oversimplification, it is often used to put one's favored ideology as far away from Hitler or Stalin. This common use of a fallacy similar to the straw man makes this chart evil.

Like the USDA soil chart, the political compass has actually been [https://knowyourmeme.com/memes/political-compass used as an alignment chart], largely to mock the original political compass chart.
|-
|Neutral Evil
|{{w|QAPF diagram|QAPF rock diagram}}
|This diagram is used to classify coarse-grained felsic (low magnesium and iron) igneous rocks by the relative volumes of the minerals quartz, alkali feldspars, plagioclase feldspars, and feldspathoids in the rock. It consists of two ternary diagrams - quartz and feldspathoid minerals cannot coexist (they will react to form feldspars) so only three of these components will be in any given rock. Rocks in the upper triangle of the diagram contain quartz, with rocks with more quartz plotting closer to the top, while rocks in the lower triangle contain feldspathoids, with rocks with more feldspathoids plotting lower. Rocks closer to the left corner of the diagram contain more alkali feldspar and rocks closer to the right corner contain more plagioclase feldspar. The field on the diagram for granite is labeled in the comic, but each area outlined on the diagram has its own rock name (monzonite, syenite, granodiorite, etc.). All the rocks that the QAPF diagram is used to classify look superficially like granite, but their chemistry, mineralogy, and origin differ.
The QAPF diagram and the names of the more obscure rock types on it can be somewhat arcane, which may be why it is considered evil here.
|-
|Chaotic Evil
|Omnispace classifier
|The other eight diagrams shown in this comic, squished together into one, with the shapes of the diagrams corresponding to those of the originals. The diagram is labeled chaotic, since it does not have a simple geometrical shape. Probably self-referential humour, in that the diagram created for this comic is considered to be chaotically evil.
|}

An alignment chart was also featured in [[2408: Egg Strategies]], which was published exactly one year later.

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

[A 3×3 grid of squares. Each square contains a label at the top and a drawing of a chart, and each square has a caption below it. From left to right, a row at a time:]

----

Soil Chart

[describe this chart here]

* Clay
* Silty Clay
* […]

Lawful Good

----

Punnett Square

[describe this chart here]

Neutral Good

----

IPA Vowel Chart

[describe this chart here]

Chaotic Good

----

Phase Diagram

[describe this chart here]

Lawful Neutral

----

Alignment Chart

[A 3×3 grid of nine empty squares, each with an unreadable label below it.]

True Neutral

----

CIE Chromaticity Diagram

[describe this chart here]

* Green
* Yellow
* …

Chaotic Neutral

----

Political Compass

[describe this chart here]

Lawful Evil

----

QAPF Rock Diagram

[The diagram is a rhombus with each corner labeled: ‘Q’ at the top, ‘A’ at the left, ‘P’ at the right, and ‘F’ at the bottom. The diagram is divided into trapezoids and triangles, each with labels. The writing in most subdivisions are unreadable. The readable subdivisions:]
* Granite (around the top left)
* Basalt (just below the right corner)
* Foidolite (at the bottom)

Neutral Evil

----

Omnispace Classifier

Chaotic Evil

[describe this chart here]

{{comic discussion}}



[[Category:Charts]]
[[Category:Biology]]
[[Category:Chemistry]]
[[Category:Physics]]
[[Category:Geology]]
[[Category:Language]]
[[Category:Fiction]]
[[Category:Politics]]
[[Category:Recursion]]

927: Standards

2020-03-31T18:39:26Z

Netjeff:

{{comic
| number = 927
| date = July 20, 2011
| title = Standards
| image = standards.png
| titletext = Fortunately, the charging one has been solved now that we've all standardized on mini-USB. Or is it micro-USB? Shit.
}}

==Explanation==
For any engineering task, there are numerous ways a given problem can be solved. The more complex the task, the more room for diversity. That's all well and good for a one-off problem, but if a design is meant to be iterated over time, or if an entire industry is solving that same problem, part reuse and {{w|interoperability}} become issues to deal with. {{w|Technical standards}} thus came to exist so that industries could avoid wasting resources {{w|reinventing the wheel}}, whilst offering their clients a certain amount of simplicity and compatibility between vendors.

But, standards have issues of their own. They don't accommodate every {{w|Use Case|use case}}, they might have restrictions or royalties attached, and people tend to be plagued by ''{{w|Not invented here|Not Invented Here syndrome}}''. So, competing standards have a tendency to arise to address different perceived needs. After a while, the market for competing standards gets messy and hard to follow, and {{w|system integration|integrating systems}} built around competing standards gets burdensome. As a result, someone eventually takes on the challenge of creating a universal standard that everyone can rally around.

This almost never works. In many cases, a new standard fails to displace the incumbent standards, eventually loses funding and support, and thus becomes a relic of history. In many other cases, it only penetrates far enough to survive, ironically making the situation messier. The latter situation often ends up becoming cyclical, with new standards periodically rising and failing to gain traction.

Three examples are given at the top of the comic: {{w|AC adapter|AC chargers}}, {{w|character encoding}} and {{w|instant messaging}}.
* Power adapters are notorious for varying from device to device - partly to try to prevent dangerous voltage/current mismatches, but partly just because manufacturers all chose different adapter designs. Mobile phone chargers have mostly converged on a common USB-based solution, but laptop charging is still a long way out, despite the adoption of yet another standard, {{w|IEC 62700}}. Randall notes that there was initially additional complexity due to the fact that there were also ''competing USB types'', but thanks to the European Union's {{w|common external power supply}} specification, micro-USB comprehensively won the day. Three years after the release of this comic, in August 2014 the {{w|USB Type-C}} specification was published and may displace micro-USB, it's gaining ground among laptop manufacturers as well.
* Character encoding is, in theory, a solved problem - {{w|Unicode}} is a standard for character sets which currently includes over 135,000 characters. However, Unicode is not an encoding, just an abstract representation of the characters, and there are several implementations which encode Unicode "code points" into usable characters (including the two most common, {{w|UTF-8}} and {{w|UTF-16}}). Despite the [https://w3techs.com/technologies/history_overview/character_encoding/ms/y success of UTF-8 Unicode ], older encodings like {{w|Windows-1252}} have stuck around, continuing to cause weird bugs in old software and websites to this day.
* Unlike the other examples, there has been little or no effort by instant messaging companies to make their services interoperable. There's more value to keeping IM as a {{w|closed platform}} so users are forced to use the company's software to access it. Some software, like the {{w|Trillian (software)|Trillian}} chat client, can connect to multiple different services, but there is essentially no way to, for example, send a Twitter message directly to a Skype user.

The title text mentions mini-USB and micro-USB, which were different standards used in 2011. As of 2019 for most applications of small USB ports (especially for charging / connecting cell phones), mini USB has lost most of its relevance and micro USB is competing with USB-C, as well as some solutions only used by single companies (such as Apple) who do not care for standards.

==Transcript==
:How Standards Proliferate
:(See: A/C chargers, character encodings, instant messaging, etc.)

:Situation:
:There are 14 competing standards.

:Cueball: 14?! Ridiculous! We need to develop one universal standard that covers everyone's use cases.
:Ponytail: Yeah!

:Soon:
:Situation: There are 15 competing standards.
{{comic discussion}}
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Ponytail]]